Vertical Translation of Square Root Graphs - Definition
Read this topicExplanations 3
- Vertical Translations We've already learned about the base square root graph. y=xy=\sqrt{x}y=x Now, we're going to look at vertical translations. In other words, shifting the g…
By Alex Federspiel, Joshua Siktar, Jonathan Heller, Anusha Rahman
- Applying a vertical translation to a graph drags it up or down along the yyy-axis. The amount of this translation is a constant, ccc, that we get to pick, and it can be positive…
By Joshua Siktar, Jonathan Heller, Anusha Rahman
- (Video) Vertical Translation of Square Root Graphs by Eric Stanwood This video by Eric Stanwood demonstrates how to create a vertical translation of a square root function. Summ…
By Anusha Rahman
Problems 27
- What is the equation for this graph?
- In the equation y=x+4y=\sqrt{x}+4y=x+4, the +4+4+4 shifts the square root graph...
- What's the vertical shift of this graph compared to the square root parent graph?
- What is the equation for this graph?
- How much do you need to shift the square root graph to get the graph of 2y=2x+22y=2\sqrt{x}+22y=2x+2?
- How many intersections does the graph y=f(x)y=f(x)y=f(x) of f(x)=xf(x) = \sqrt{x}f(x)=x have with its vertical translation y−10=f(x)y-10 = f(x)y−10=f(x)?
- Which of the following equations represents a shift of the graph y=xy=\sqrt{x}y=x up 333 units?
- Which of the following equations shifts the graph y=xy=\sqrt{x}y=x down 444 units?
- If you shift the graph y=xy=\sqrt{x}y=x up by 333 units and right by 222 units, what is the new equation of the graph?
- If you shift the graph y=xy=\sqrt{x}y=x down by 444 units and left by 666 units, what is the new equation of the graph?
- What is the vertical shift aaa in the graph pictured above compared to the graph of the square root?
- What is the vertical shift aaa in the graph pictured above compared to the graph of the square root?
- What is the vertical shift aaa in the graph pictured above compared to the graph of the square root?
- Select the equation of the graph that has a vertical translation of +3+3+3 units compared to the square root function.
- Select the equation of the graph that has a vertical translation of −4-4−4 units compared to the square root function.
- Select the equation of the graph that has a vertical translation of +2+2+2 units compared to the square root function.
- Consider the graph of f(x)=x+1f(x)=\sqrt{x}+1f(x)=x+1 and g(x)=x+3g(x)=\sqrt{x}+3g(x)=x+3 above. \\What is the difference ddd between f(x)f(x)f(x) and g(x)g(x)g(x) for any x≥0…
- Consider the graphs of f(x)=x+1f(x)=\sqrt{x}+1f(x)=x+1 (red) and g(x)=x−1g(x)=\sqrt{x}-1g(x)=x−1 (blue) above. \\What is the difference ddd between f(x)f(x)f(x) and g(x)g(x)g(…
- Do the graphs y=xy=\sqrt{x}y=x and y=x+ay=\sqrt{x}+ay=x+a intersect for any nonzero value of aaa?
- If f(n)=1.5f(n)=1.5f(n)=1.5 for some positive number nnn, what is the value of g(n)g(n)g(n)?
- If f(n)=4.43f(n)=4.43f(n)=4.43 for some positive number nnn, what is the value of g(n)g(n)g(n)?
- If f(n)=52f(n)=\frac{5}{2}f(n)=25 for some positive number nnn, what is the value of g(n)g(n)g(n)?
- If f(n)=94f(n)=\frac{9}{4}f(n)=49 for some positive number nnn, what is the value of g(n)g(n)g(n)?
- kkk is a positive, non-zero constant. \\ The graph of the square root function shifted upward kkk units has a function of:
- kkk is a positive, non-zero constant. The graph of the square root function shifted downward kkk units has a function of:
- The red graph is 333 units above the blue graph. If yblue=kxy_{\text{blue}} = \sqrt{kx}yblue=kx where kkk is some positive, non-zero constant, what is the function yredy_{\tex…
- yred=abx+5cy_{\text{red}} = a\sqrt{bx} + 5cyred=abx+5c Assume aaa, bbb, and ccc are positive, non-zero constants. If the red graph is only 3c3c3c above the blue one, what is t…