Shift Function Up or Down: f(x)+c
Read this topicExplanations 4
- In a quadratic equation, the yyy represents the coordinate for how high up each point on the curve is. Take a look at the 666 graphs below. They all have the same slope, or they…
By Vivian Loh, Alex Federspiel, Joshua Siktar
- Vertical Translation Translation is moving a graph around on a plane. Vertical translation is moving a graph exclusively up or down on the plane. Let's look at an example: Here …
By Ben Ferrara, Zora Gilbert, Vatsal Ojha, Caroline K, Jonathan Heller
- (Video) Translating Absolute Value Functions by Keith Mann This video by Keith Mann explains how to translate functions vertically (in other words, move them up or down on a gra…
By Ben Ferrara, Alex Federspiel, Zora Gilbert, Joshua Siktar, Caroline K, Jonathan Heller
- Vertical Translation The first lesson in our series on function transformations is vertical translations! A vertical shift allows you to move a function up or down along the yyy…
By Anusha Rahman
Problems 120
- Which is the graph of the equation y=∣x∣−4y=|x|-4y=∣x∣−4?
- If the graph of y=∣x∣+cy=|x|+cy=∣x∣+c is 111111 units below the graph of y=∣x∣y = |x|y=∣x∣, what is ccc?
- If the graph of y=∣x∣+cy=|x|+cy=∣x∣+c is 999 units above the graph of y=∣x∣y = |x|y=∣x∣, what is ccc?
- How would you move the graph of y=∣x∣y = |x|y=∣x∣ to the graph of y=∣x∣−3?y=|x| - 3?y=∣x∣−3?
- How would you move the graph of y=∣x∣y = |x|y=∣x∣ to the graph of y=∣x∣+22?y=|x| + 22?y=∣x∣+22?
- The function f(x)=1xf(x) = \frac{1}{x}f(x)=x1 never touches the xxx-axis. What is the maximum amount you could shift this function vertically and still have it not touch the xx…
- Describe how the function f(x−49)f(x-49)f(x−49) is a transformation of the original function f(x)f(x)f(x).
- Describe how f(x+43)f(x+43)f(x+43) is a transformation of the original function f(x)f(x)f(x).
- Describe how each function is a transformation of the original function f(x)f(x)f(x) f(x+3)f(x+3)f(x+3)
- Describe how f(x−4)f(x-4)f(x−4) is a transformation of the original function f(x)f(x)f(x).
- Describe how the following function is a transformation of the original function f(x)f(x)f(x). f(x)+5f(x)+5f(x)+5
- Describe how f(x)+8f(x)+8f(x)+8 is a transformation of the original function f(x)f(x)f(x).
- Describe how each function is a transformation of the original function f(x)f(x)f(x) f(x)−2f(x)-2f(x)−2
- Describe how f(x)−7f(x)-7f(x)−7 is a transformation of the original function f(x)f(x)f(x).
- Describe how f(x−2)+3f(x-2)+3f(x−2)+3 is a transformation of the original function f(x)f(x)f(x). Select all correct answers.
- Describe how f(x+4)−1f(x+4)-1f(x+4)−1 is a transformation of the original function f(x).f(x).f(x).
- Write a formula for f(x)=xf(x)=\sqrt xf(x)=x shifted up 111 unit and left 222 units.
- Write a formula for f(x)=∣x∣f(x)=|x|f(x)=∣x∣ shifted down 333 units and right 111 unit.
- Write a formula for f(x)=1xf(x)=\dfrac1xf(x)=x1 shifted down 444 units and right 333 units.
- Write a formula for f(x)=1x2f(x)=\dfrac1{x^2}f(x)=x21 shifted up 222 units and left 444 units.
- Tables of values for f(x)f(x)f(x), g(x)g(x)g(x), and h(x)h(x)h(x) are given above. Write g(x)g(x)g(x) and h(x)h(x)h(x) as transformations of f(x)f(x)f(x).
- Tables of values for f(x)f(x)f(x), g(x)g(x)g(x), and h(x)h(x)h(x) are given above. Write g(x)g(x)g(x) and h(x)h(x)h(x) as transformations of f(x)f(x)f(x).
- The graph f(x)=2xf(x)=2^xf(x)=2x is shown along with a transformation. Which function below represents the transformation shown above?
- The graph f(x)=2xf(x)=2^xf(x)=2x is shown along with a transformation. Which function below represents the transformation shown above?
- g(t)=t2g(t)=t^2g(t)=t2 is graphed above along with a transformation. What function below represents the transformation above?
- f(x)=x3f(x)=x^3f(x)=x3 is graphed above along with a transformation. What function below represents the transformation above?
- Which equation represents the function graphed above?
- Which equation represents the function graphed above?
- Which equation represents the function graphed above?
- Which equation represents the function graphed above?
- The graph above is a transformation of the parent graph f(x)=xf(x)=\sqrt{x}f(x)=x. Which function represents that transformation?
- The graph above is a transformation of the parent graph f(x)=xf(x)=\sqrt{x}f(x)=x. Which function represents that transformation?
- f(x)=2xf(x)=2^xf(x)=2x is graphed above along with its transformation. Which function below represents the transformation above?
- Starting with the graph of f(x)=6xf(x)=6^xf(x)=6x write the equation of the graph that results from reflecting f(x)f(x)f(x) about the xxx-axis and the yyy-axis.
- Starting with the graph of f(x)=6xf(x)=6^xf(x)=6x write the equation of the graph that results from reflecting f(x)f(x)f(x) about the yyy-axis, shifting right 444 units and up 2…
- Starting with the graph of f(x)=4xf(x)=4^xf(x)=4x write the equation of the graph that results from reflecting f(x)f(x)f(x) about the xxx-axis.
- Starting with the graph of f(x)=4xf(x)=4^xf(x)=4x write the equation of the graph that results from reflecting f(x)f(x)f(x) about the yyy-axis, shifting right 444 units and up 2…
- Which equation represents the function graphed above.
- Which equation represents the function graphed above.
- Which equation represents the function graphed above.
- Which equation represents the function graphed above?
- Is f(x)=3x4f(x)=3x^4f(x)=3x4 Odd, Even, or Neither?
- Is g(x)=xg(x)=\sqrt xg(x)=x Odd, Even, or Neither.
- Is h(x)=1x+3xh(x)=\dfrac1x+3xh(x)=x1+3x Odd, Even, or Neither.
- Is f(x)=(x−2)2f(x)=(x-2)^2f(x)=(x−2)2 Odd, Even, or Neither.
- Is g(x)=2x4g(x)=2x^4g(x)=2x4 Odd, Even, or Neither.
- Is h(x)=2x−x3h(x)=2x-x^3h(x)=2x−x3 Odd, Even, or Neither.
- Write the function f(x)f(x)f(x) after the transformation. Reflection over the xxx-axis
- Write the function f(x)f(x)f(x) after the transformation. Reflection over the yyy-axis
- Write the function f(x)f(x)f(x) after the transformation. Vertically stretch the function by a factor of 4
- Write the function f(x)f(x)f(x) after the transformation. Vertical Stretch by a factor of 666
- Write the function f(x)f(x)f(x) after the transformation. Horizontal stretch by a factor of 5
- Write the function f(x)f(x)f(x) after the transformation. Horizontal stretch by a factor of 333
- Write the function f(x)f(x)f(x) after the transformation. Horizontal compression by a factor of 15\frac1551
- Write the function f(x)f(x)f(x) after the transformation. Horizontal compression by a factor of 12\frac1221
- Write the function f(x)f(x)f(x) after the transformation. Vertical Stretch by a factor of 333 Reflection over the yyy-axis
- Write the function f(x)f(x)f(x) after the transformation. Horizontal compression by a factor of 13\frac1331 Reflection over the xxx axis
- Write the function f(x)f(x)f(x) after the transformation. f(x)=∣x∣f(x)=|x|f(x)=∣x∣ Reflected over the yyy-axis Horizontally compressed by a factor of 14\frac1441
- Write the function f(x)f(x)f(x) after the transformation. f(x)=xf(x)=\sqrt xf(x)=x Reflected over the xxx-axis Horizontally stretched by a factor of 222
- f(x)=x2f(x)=x^2f(x)=x2 Vertically stretched by 444 Shifted right 111 Shifted down 555 → f(x)=4(x+1)2−5\rightarrow\;f(x)=4(x+1)^2-5→f(x)=4(x+1)2−5
- Write the function f(x)f(x)f(x) after the transformation. f(x)=1xf(x)=\dfrac1{x}f(x)=x1 Shifted right 444 Shifted up 222
- Write the function f(x)f(x)f(x) after the transformation. f(x)=1x2f(x)=\dfrac1{x^2}f(x)=x21 Vertically compressed by a factor of 13\frac1331 Shifted left 222 Shifted down 333
- Write the function f(x)f(x)f(x) after the transformation. f(x)=x2f(x)=x^2f(x)=x2 Horizontally compressed by a factor of 12\frac1221 Shifted right 555 Shifted up 111
- Write the function f(x)f(x)f(x) after the transformation. f(x)=x2f(x)=x^2f(x)=x2 Horizontally stretched by a factor of 333 Shifted left 444 Shifted down 333
- f(x)=x2f(x)=x^2f(x)=x2 Vertically stretched by 555 Shifted left 333 Shifted down 222 → f(x)=5(x+3)2−2\rightarrow\;f(x)=5(x+3)^2-2→f(x)=5(x+3)2−2
- f(x)=∣x∣f(x)=|x|f(x)=∣x∣ Reflected over the x axis Vertically stretched by 222 Shifted right 444 Shifted up 333 → f(x)=−2∣x−4∣+3\rightarrow\;f(x)=-2|x-4|+3→f(x)=−2∣x−4∣+3
- f(x)=xf(x)=\sqrt xf(x)=x Reflected over the xxx axis Vertically stretched by 333 Shifted right 111 → f(x)=−3x−1\rightarrow\;f(x)=-3\sqrt x-1→f(x)=−3x−1
- f(x)=x3f(x)=x^3f(x)=x3 Vertically compressed by a factor of 12\frac1221 → f(x)=12x3\rightarrow\;f(x)=\dfrac12x^3→f(x)=21x3
- f(x)=∣x∣f(x)=|x|f(x)=∣x∣ Vertically stretched by a factor of 13\frac1331 Shifted left 222 → f(x)=13∣x−2∣\rightarrow\;f(x)=\dfrac13|x-2|→f(x)=31∣x−2∣
- f(x)=x2f(x)=x^2f(x)=x2 Vertically stretched by a factor of 13\frac1331 Shifted down 333 → f(x)=(13x)2−3\rightarrow\;f(x)=\begin{pmatrix}\dfrac13x\end{pmatrix}^2-3→f(x)=(31x)2−3
- True or False? f(x)=x3f(x)=x^3f(x)=x3 horizontally stretched by a factor of 444 and shifted up 111 is: f(x)=(14x)3+1f(x)=\begin{pmatrix}\dfrac14x\end{pmatrix}^3+1f(x)=(41x)3+1
- f(x)=xf(x)=\sqrt xf(x)=x Reflected over the yyy-axis Shifted left 444 → f(x)=−x+4\rightarrow\;f(x)=\sqrt{-x+4}→f(x)=−x+4
- True or False\text{True or False}True or False f(x)=x3f(x)=\sqrt[3] xf(x)=3x Reflected over the yyy-axis Shifted right 666 → f(x)=−x−63\rightarrow\;f(x)=\sqrt[3]{-x-6}→f(x)=3−x−6
- Determine the interval(s) on which the function is increasing and decreasing. Select all correct answers. f(x)=4(x+1)2−5f(x)=4(x+1)^2-5f(x)=4(x+1)2−5
- Determine the interval(s) on which the function is increasing and decreasing. f(x)=5(x+3)2−2f(x)=5(x+3)^2-2f(x)=5(x+3)2−2
- Determine the interval(s) on which the function is increasing and decreasing. f(x)=−x+4f(x)=\sqrt{-x+4}f(x)=−x+4
- Determine the interval(s) on which the function is increasing and decreasing. f(x)=−3x−1f(x)=-3\sqrt{x}-1f(x)=−3x−1
- Determine the interval(s) on which the function is concave up and concave down f(x)=−2(x+3)3+1f(x)=-2(x+3)^3+1f(x)=−2(x+3)3+1
- Determine the interval(s) on which the function is concave up and concave down f(x)=−x−63f(x)=\sqrt[3]{-x-6}f(x)=3−x−6
- Determine the interval(s) on which the function is concave up and concave down f(x)=(13x)2−3f(x)=\begin{pmatrix}\dfrac13x\end{pmatrix}^2-3f(x)=(31x)2−3
- Determine the interval(s) on which the function is concave up and concave down f(x)=−3x−1f(x)=-3\sqrt x-1f(x)=−3x−1
- What would we have to do to change the graph above to show the function f(x)=∣x−3∣+2f\left(x\right)=\left|x-3\right|+2f(x)=∣x−3∣+2?
- A vertical translation concerning a graph of a function represents a shift
- If f(x)=∣x∣f(x)=|x|f(x)=∣x∣, then ______ gives a vertical translation.
- What function is represented above?
- Which color curve represents the function f(x)=∣x2∣+1f\left(x\right)=\left|x^2\right|+1f(x)=x2+1?
- In the function y=∣x∣+ky=|x|+ky=∣x∣+k, what is the parent function?
- Which of the colors represents a negative vertical shift for the function f(x)=−∣x∣f(x)=-|x|f(x)=−∣x∣?
- Which of the following represents a vertical shift up?
- What function is represented above?
- Write the equation of the graph shown.
- A developer's project has been put on hold because he violated code by crossing property lines. The property line is represented by y=xy=xy=x and his projected building location…
- Write the equation of the absolute value function that opens down and shifts g(x)=∣x∣g(x)=|x|g(x)=∣x∣ vertically up 555 units.
- Which of the following represents a vertical shift down?
- Which of the following represents f(x)=∣x−4∣+7f(x)=|x-4|+7f(x)=∣x−4∣+7 being shifted down by 999 units?
- What equation represents a vertical translation of f(x)=∣x∣?f(x) = |x|?f(x)=∣x∣?
- If the graph of y=∣x∣y=|x|y=∣x∣ is shifted down by 444 units, where does the new (shifted) graph intersect the xxx-axis?
- Let a≠0a \neq 0a=0 be a real number. How many times do the graphs f(x)=∣x∣f(x) = |x|f(x)=∣x∣ and g(x)=∣x∣+ag(x) = |x| + ag(x)=∣x∣+a intersect?
- You have the graph of y=∣x∣y = |x|y=∣x∣ and decide to make another graph, for a function z,z,z, where you randomly do a horizontal translation of yyy of size −1,0,-1, 0,−1,0, or…
- You are shifting the graph of the function y=∣x∣y = |x|y=∣x∣ downward by a random amount: either by 111 unit, 222 units, or 333 units. Regardless of which one you choose, a tria…
- True or False\text{True or False}True or False === The function f(x)=1xf(x)= \frac{1}{x}f(x)=x1 is graphed above in red. The function in blue is f(x)+cf(x)+cf(x)+c when c=2c=2c=2.
- If g(x)g(x)g(x) is the vertical shift down of 222 units from f(x)f(x)f(x) and f(x)=7x+3f(x)=7x+3f(x)=7x+3, what is g(x)g(x)g(x)?
- f(x)=3x3−1f(x)=3x^3-1f(x)=3x3−1 and g(x)g(x)g(x) is f(x)f(x)f(x) shifted up 111 units. Is g(x)g(x)g(x) an even function, odd function, or neither?
- Describe how the function f(x)=13x4−x2−3f(x)=\frac{1}{3}x^4-x^2-3f(x)=31x4−x2−3 is shifted to get g(x)=13x4−x2+7g(x)=\frac{1}{3}x^4-x^2+7g(x)=31x4−x2+7.
- Given f(x)=xf(x)=xf(x)=x, which of the following functions represent vertical shifts?
- The following table shows the inputs and outputs for the function f(x)f(x)f(x). Which of the following functions are vertical shifts of f(x)f(x)f(x)? x0123456789f(x)246810121416…
- Which of the following set of functions show a vertical shift?
- True or False\text{True or False}True or False === The function f(x)=x7+2f(x)=x^7+2f(x)=x7+2 is graphed in blue above. The red function is the vertical shift up 222 units from f…
- Given f(x)=3xf(x)=3\sqrt{x}f(x)=3x, what is g(x)g(x)g(x) when g(x)g(x)g(x) is f(x)f(x)f(x) that is vertically shifted down 32\frac{3}{2}23 units?
- f(x)=∣12x∣−1f(x)=|\frac{1}{2}x|-1f(x)=∣21x∣−1 and g(x)g(x)g(x) is f(x)f(x)f(x) shifted down 333 units. Is g(x)g(x)g(x) an even function, odd function, or neither?
- Describe how the function f(x)=∣x∣−3f(x)=|x|-3f(x)=∣x∣−3 is shifted to get g(x)=3(∣13x∣−13)g(x)=3(|\frac{1}{3}x|-\frac{1}{3})g(x)=3(∣31x∣−31).
- Given f(x)=x3f(x)=x^3f(x)=x3, which of the following functions represent vertical shifts?
- Given f(x)=∣x∣f(x)=|x|f(x)=∣x∣, which of the following functions represent vertical shifts?
- True or False\text{True or False}True or False === The graph above shows the function f(x)=∣x−4∣f(x)=|x-4|f(x)=∣x−4∣ in red. The function graphed in blue is a vertical shift of …
- Which of the following tables are a vertical shift of the function f(x)f(x)f(x)? The table for f(x)f(x)f(x) is: x0123456789f(x)712364891114\begin{array}{|l|l|} \hline x&0&1&2&3&…
- Which of the following functions are a vertical translation of the function f(x)=3(x−2)2+3f(x)=3(x-2)^2+3f(x)=3(x−2)2+3.
- Which of the following functions are a vertical translation of the function f(x)=x−2f(x)=\sqrt{x-2}f(x)=x−2?
- f(x)=12x2f(x)=\frac{1}{2}x^2f(x)=21x2 and g(x)g(x)g(x) is f(x)f(x)f(x) shifted down 12\frac{1}{2}21 units. Is g(x)g(x)g(x) an even function, odd function, or neither?
- Which of the following set of functions show a vertical shift?
- Describe how you would obtain the function f(x)=(x−2)3−13f(x)=(x-2)^3 - \frac{1}{3}f(x)=(x−2)3−31, starting with the function f(x)=(x−2)3f(x)=(x-2)^3f(x)=(x−2)3.