Shift Function Left or Right: f(x+c)
Read this topicExplanations 4
- Graphs of f(x+c)f(x+c)f(x+c) Pretend you had some nasty function f(x)f(x)f(x) and you just finished figuring out how it works. But then the teacher tells everybody, "Graph f(x+3…
By Ivan Hu, Alex Federspiel, Joshua Siktar
- When moving a function right or left, you change the xxx coordinate. For example, take f(x)=x2f(x) = x^2f(x)=x2 and move it to the left: The only thing changing, is the xxx coor…
By Bladyda, Joshua Siktar
- In Context In this series of function transformations, we are starting off with vertical and horizontal translations. This lesson will consider the horizontal transformations. H…
By Anusha Rahman
- (Video) Horizontal Function Transformations by Anusha Rahman In this lesson by Anusha Rahman, you will learn about shifting a function to the left or right. Summary A horizontal…
By Anusha Rahman
Problems 44
- Which is the graph of the equation y=∣x+4∣y=|x+4|y=∣x+4∣?
- If the graph of y=∣x+c∣y=|x+c|y=∣x+c∣ is 777 units to the right of the graph of y=∣x∣y = |x|y=∣x∣, what is ccc?
- If the graph of y=∣x+c∣y=|x+c|y=∣x+c∣ is 5 units to the left of 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−6∣?y=|x-6|?y=∣x−6∣?
- How would you move the graph of y=∣x∣y = |x|y=∣x∣ to the graph of y=∣x+12∣y=|x+12|y=∣x+12∣?
- Suppose f(x)=ax+bf(x) = ax + bf(x)=ax+b. What is f(x+c)f(x + c)f(x+c)?
- Suppose f(x)=bxf(x) = b^xf(x)=bx for some constant bbb. What is f(x+c)f(x + c)f(x+c)?
- Suppose fff is a function which satisfies f(x+c)=f(x)+cf(x + c) = f(x) + cf(x+c)=f(x)+c. Which type of function could fff be?
- Suppose fff is a function which satisfies f(x+c)=c⋅f(x)f(x + c) = c \cdot f(x)f(x+c)=c⋅f(x). Which type of function must fff be?
- Let f(x)=x5−3x+1f(x) = x^5 - 3^{x+1}f(x)=x5−3x+1. Let ggg be fff shifted two units to the right. What is g(4)g(4)g(4)?
- Let f(x)f(x)f(x) be a real function, and g(x)=f(x+1)g(x) = f(x+1)g(x)=f(x+1). Suppose the minimum value of fff is mmm. What is the minimum value of ggg?
- Let f(x)=2xf(x)=2^xf(x)=2x and let c=3c=3c=3. What is the graph of f(x+c)f(x+c)f(x+c)?
- Let f(x)=3xf(x)=3xf(x)=3x and let c=5c=5c=5. What is the graph of f(x+c)f(x+c)f(x+c)?
- Let f(x)=x3f(x)=x^3f(x)=x3 and let c=−2c=-2c=−2. What is the graph of f(x+c)f(x+c)f(x+c)?
- True or False: If f(x)=x2f(x)=x^2f(x)=x2 and c=3c=3c=3, then f(x+c)f(x+c)f(x+c) is graphed above.
- True or False: If f(x)=1x+2f(x)=\frac1x+2f(x)=x1+2 and c=−2c=-2c=−2, then f(x+c)f(x+c)f(x+c) is graphed above.
- True or False: If f(x)={−12x−32−4≤x<−1x3−1≤x≤2f(x)=\begin{cases}-\frac12x-\frac32&-4\leq x<-1\\x^3&-1\leq x\leq2\end{cases}f(x)={−21x−23x3−4≤x<−1−1≤x≤2 and c=12c=\frac12c=21…
- 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?
- What function is represented above?
- Consider the absolute value function f(x)=∣x∣f\left(x\right)=\left|x\right|f(x)=∣x∣. Which function represents a horizontal shift in this function?
- Let f(x)=∣x∣f(x) = |x|f(x)=∣x∣, and let g(x)g(x)g(x) be a horizontal translation g(x)=f(x−h)g\left(x\right)=f\left(x-h\right)g(x)=f(x−h). In order for g(x)g(x)g(x) to be a shift…
- What needs to be true in order for the function g(x)=∣x−h∣g(x)=|x-h|g(x)=∣x−h∣ to shift the absolute value function f(x)=∣x∣f(x) = |x|f(x)=∣x∣ to the left?
- A horizontal translation concerning a graph represents a shift
- Which color line represents the function f(x)=∣x+2−1∣f(x)=|x+2-1|f(x)=∣x+2−1∣?
- What function does the graph above represent?
- Which function is represented in red?
- Which of the following represents the shifts from f(x)=−∣x∣f(x)=-|x|f(x)=−∣x∣ to f(x)=∣x+1∣f(x)=|x+1|f(x)=∣x+1∣ to f(x)=−∣x−1∣f(x)=-|x-1|f(x)=−∣x−1∣?
- Which is the graph of the equation y=−∣x+9∣y=-|x+9|y=−∣x+9∣?
- Which of the following represents f(x)=∣x−4∣+7f(x)=|x-4|+7f(x)=∣x−4∣+7 being shifted to the right 999 units?
- Write the equation of the absolute value function that opens up and shifts g(x)=∣x∣g(x)=|x|g(x)=∣x∣ to the left by 2.52.52.5 units.
- How would you move the graph y=∣x∣y=|x|y=∣x∣ to the graph y=∣x−7∣y=|x-7|y=∣x−7∣?
- Which of the following represents a horizontal shift to the right?
- Which equation represents a horizontal translation of y=∣x∣y=|x|y=∣x∣?
- For a real number a≠0a \neq 0a=0 define f(x)=∣x∣f(x) = |x|f(x)=∣x∣ and g(x)=∣x−a∣g(x) = |x-a|g(x)=∣x−a∣. How many times do the graphs of f(x)f(x)f(x) and g(x)g(x)g(x) 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…
- f(x)f(x)f(x) is defined by f(x)=−3x2−4x+11f(x)= -3x^2-4x+11f(x)=−3x2−4x+11. Find f(x−2)f(x-2)f(x−2).
- Consider the two following functions: \\ f(x)=x2f(x) = x^2f(x)=x2 and g(x)=(x−6)2g(x)= (x-6)^2g(x)=(x−6)2\\ How is the function g(x)g(x)g(x) shifted compared to f(x)f(x)f(x)?
- Shift the following equation to the right by 666: f(x)=x+8f(x)= x+8f(x)=x+8
- Given the function f(x)=x3f(x)=x^3f(x)=x3, write the equation of the new function g(x)g(x)g(x) that has been shifted to the left by 555 units.
- Consider the two following functions: \\ f(x)=∣x∣f(x)=|x|f(x)=∣x∣ and g(x)=∣x+10∣g(x)= |x+10|g(x)=∣x+10∣ \\ How is the function g(x)g(x)g(x) shifted compared to f(x)f(x)f(x)?
- f(x)f(x)f(x) is defined by f(x)=2x+7f(x)=2x+7f(x)=2x+7. Find g(3)g(3)g(3) if g(x)g(x)g(x) is the function of f(x)f(x)f(x) shifted to the right by 444 units.
- Shift the following equation to the left by 777: f(x)=−x2−x−3f(x)= -x^2-x-3f(x)=−x2−x−3
- The function f(x)f(x)f(x) is graphed above. Which of the answer choices is a graph of f(x+1)f(x+1)f(x+1)?
- For what value(s) of ccc are a leftward shift by ccc units and a rightward shift by ccc units the same transformation?