# Transformations - Video Tutorials & Practice Problems

## Intro to Transformations

## Reflections of Functions

## Reflections of Functions Example 1

Written below (green dotted curve)** **is a graph of the function ï»¿$f\left(x\right)=\sqrt{x-2}$ï»¿. If

**(blue solid curve) is a reflection of**

*g(x)***about the**

*f(x)***what is the equation for**

*y-axis***?**

*g(x)*ï»¿$g\left(x\right)=\sqrt{-x-2}$ï»¿

ï»¿$g\left(x\right)=\sqrt{-x}-2$ï»¿

ï»¿$g\left(x\right)=\sqrt{x-2}$ï»¿

ï»¿$g\left(x\right)=\sqrt{x}-2$ï»¿

## Shifts of Functions

The green dotted line in the graph below represents the function ï»¿$f\left(x\right)$ï»¿. The blue solid line represents the function ï»¿$g\left(x\right)$ï»¿, which is the function ï»¿$f\left(x\right)$ï»¿ after it has gone through a shift transformation. Find the equation for ï»¿$g\left(x\right)$ï»¿.

ï»¿$g\left(x\right)=f\left(x-2\right)+3$ï»¿

ï»¿$g\left(x\right)=f\left(x-2\right)-3$ï»¿

ï»¿$g\left(x\right)=f\left(x+2\right)-3$ï»¿

ï»¿$g\left(x\right)=f\left(x\right)-3$ï»¿

## Graphs of Shifted & Reflected Functions

## Graphs of Shifted & Reflected Functions Example 1

## Stretches & Shrinks of Functions

## Stretches & Shrinks of Functions Example 1

## Domain & Range of Transformed Functions

The green dotted curve below is a graph of the function ï»¿$f\left(x\right)$ï»¿. Find the domain and range of ï»¿$g\left(x\right)$ï»¿ (the blue solid curve), which is a transformation of ï»¿$f\left(x\right)$ï»¿.

**Dom: ï»¿$\left[1,4\right]$ï»¿ , Ran: **ï»¿$\left[-5,-1\right]$ï»¿

**Dom: ï»¿$\left[1,5\right]$ï»¿ , Ran: **ï»¿$\left[-5,1\right]$ï»¿

**Dom: ï»¿$\left[-1,3\right]$ï»¿ , Ran: **ï»¿$\left[-2,4\right]$ï»¿

**Dom: ï»¿$\left[-2,3\right]$ï»¿ , Ran: **ï»¿$\left[2,4\right]$ï»¿

## Do you want more practice?

- In Exercises 1-16, use the graph of y = f(x) to graph each function g. g(x) = f(x)+1
- In Exercises 1-16, use the graph of y = f(x) to graph each function g. g(x) = f(x+1)
- In Exercises 1-16, use the graph of y = f(x) to graph each function g. g(x) = f(-x)
- In Exercises 1-16, use the graph of y = f(x) to graph each function g. g(x) = -f(x) +3
- In Exercises 1-16, use the graph of y = f(x) to graph each function g. g(x) = f(-x)+3
- In Exercises 1-16, use the graph of y = f(x) to graph each function g. g(x) = 2f(x)
- In Exercises 1-16, use the graph of y = f(x) to graph each function g. g(x) = f(x/2)
- In Exercises 1-16, use the graph of y = f(x) to graph each function g. g(x) = -f(2x) - 1
- Graph each function. See Examples 1 and 2. Æ’(x)=3|x|
- In Exercises 17-32, use the graph of y = f(x) to graph each function g. g(x) = f(x) - 1
- In Exercises 17-32, use the graph of y = f(x) to graph each function g. g(x) = f(x-1)
- Graph each function. See Examples 1 and 2. Æ’(x)=2/3|x|
- In Exercises 17-32, use the graph of y = f(x) to graph each function g. g(x) = f(x-1)+2
- In Exercises 17-32, use the graph of y = f(x) to graph each function g. g(x) = f(x + 1) âˆ’ 2
- Graph each function. See Examples 1 and 2. g(x)=(1/2)x^2
- In Exercises 17-32, use the graph of y = f(x) to graph each function g. g(x) = f(-x)
- Graph each function. See Examples 1 and 2. Æ’(x)=-(1/2)x^2
- In Exercises 17-32, use the graph of y = f(x) to graph each function g. g(x) = f(-x)+1
- In Exercises 17-32, use the graph of y = f(x) to graph each function g. g(x) = -f(x)+1
- Graph each function. See Examples 1 and 2. Æ’(x)=-3|x|
- In Exercises 17-32, use the graph of y = f(x) to graph each function g. g(x) = Â½ f(x)
- Graph each function. See Examples 1 and 2. h(x)=|-(1/2)x|
- Graph each function. See Examples 1 and 2. h(x)=âˆš(4x)
- In Exercises 33-44, use the graph of y = f(x) to graph each function g. g(x) = f(x)+2
- Graph each function. See Examples 1 and 2. Æ’(x)=-âˆš-x
- In Exercises 33-44, use the graph of y = f(x) to graph each function g. g(x) = f(x+2)
- Plot each point, and then plot the points that are symmetric to the given point with respect to the (a) x-axis...
- In Exercises 33-44, use the graph of y = f(x) to graph each function g. g(x) = -(1/2)f(x+2)
- Plot each point, and then plot the points that are symmetric to the given point with respect to the (a) x-axis...
- In Exercises 33-44, use the graph of y = f(x) to graph each function g. g(x) = -Â½ Æ’ ( x + 2) â€”2
- In Exercises 33-44, use the graph of y = f(x) to graph each function g. g(x) = (1/2)f(2x)
- Without graphing, determine whether each equation has a graph that is symmetric with respect to the x-axis, th...
- In Exercises 45-52, use the graph of y = f(x) to graph each function g. g(x) = -f(x-1) + 1
- Without graphing, determine whether each equation has a graph that is symmetric with respect to the x-axis, th...
- In Exercises 45-52, use the graph of y = f(x) to graph each function g. g(x) = -f(x + 1) âˆ’ 1
- In Exercises 45-52, use the graph of y = f(x) to graph each function g. g(x)=2f(x-1)
- In Exercises 53-66, begin by graphing the standard quadratic function, f(x) = xÂ². Then use transformations of ...
- In Exercises 53-66, begin by graphing the standard quadratic function, f(x) = xÂ². Then use transformations of ...
- In Exercises 55â€“59, use the graph of to graph each function g. g(x) = f(x + 2) + 3
- In Exercises 55â€“59, use the graph of to graph each function g. g(x) = -f(2x)
- In Exercises 60â€“63, begin by graphing the standard quadratic function, f(x) = x^2. Then use transformations of...
- In Exercises 60â€“63, begin by graphing the standard quadratic function, f(x) = x^2. Then use transformations of...
- In Exercises 53-66, begin by graphing the standard quadratic function, f(x) = xÂ². Then use transformations of ...
- In Exercises 64â€“66, begin by graphing the square root function, f(x) = âˆšx. Then use transformations of this gr...
- In Exercises 64â€“66, begin by graphing the square root function, f(x) = âˆšx. Then use transformations of this gr...
- Graph each function. See Examples 6â€“8 and the Summary of Graphing Techniques box following Example 9. Æ’(x)=x^2...
- In Exercises 67-80, begin by graphing the square root function, f(x) = âˆšx. Then use transformations of this gr...
- In Exercises 67-80, begin by graphing the square root function, f(x) = âˆšx. Then use transformations of this gr...
- In Exercises 67-80, begin by graphing the square root function, f(x) = âˆšx. Then use transformations of this gr...
- Consider the following nonlinear system. Work Exercises 75 â€“80 in order. y = | x - 1 | y = x^2 - 4 How is the...
- Graph each function. See Examples 6â€“8 and the Summary of Graphing Techniques box following Example 9. h(x)=-(x...
- Graph each function. See Examples 6â€“8 and the Summary of Graphing Techniques box following Example 9. Æ’(x)=-3(...
- In Exercises 81â€“94, begin by graphing the absolute value function, f(x) = |x|. Then use transformations of thi...
- In Exercises 81â€“94, begin by graphing the absolute value function, f(x) = |x|. Then use transformations of thi...
- Graph each function. See Examples 6â€“8 and the Summary of Graphing Techniques box following Example 9. Æ’(x)=2âˆšx...
- In Exercises 81â€“94, begin by graphing the absolute value function, f(x) = |x|. Then use transformations of thi...
- Graph each function. See Examples 6â€“8 and the Summary of Graphing Techniques box following Example 9. Æ’(x)=3âˆšx...
- What is the relationship between the graphs of Æ’(x)=|x| and g(x)=|-x|?
- Each of the following graphs is obtained from the graph of Æ’(x)=|x| or g(x)=âˆšx by applying several of the tran...
- In Exercises 95-106, begin by graphing the standard cubic function, f(x) = xÂ³. Then use transformations of thi...
- Describe how the graph of each function can be obtained from the graph of Æ’(x) = |x|. g(x) = -|x|
- In Exercises 95-106, begin by graphing the standard cubic function, f(x) = xÂ³. Then use transformations of thi...
- Let Æ’(x) = 3x -4. Find an equation for each reflection of the graph of Æ’(x). across the x-axis
- In Exercises 95-106, begin by graphing the standard cubic function, f(x) = xÂ³. Then use transformations of thi...
- Let Æ’(x) = 3x -4. Find an equation for each reflection of the graph of Æ’(x). across the y-axis
- Each of the following graphs is obtained from the graph of Æ’(x)=|x| or g(x)=âˆšx by applying several of the tran...
- The graph of a function Æ’ is shown in the figure. Sketch the graph of each function defined as follows. (a) ...
- The graph of a function Æ’ is shown in the figure. Sketch the graph of each function defined as follows. (b) ...
- The graph of a function Æ’ is shown in the figure. Sketch the graph of each function defined as follows. (c) ...
- The graph of a function Æ’ is shown in the figure. Sketch the graph of each function defined as follows. (d) ...
- In Exercises 107-118, begin by graphing the cube root function, f(x) = âˆ›x. Then use transformations of this gr...
- In Exercises 107-118, begin by graphing the cube root function, f(x) = âˆ›x. Then use transformations of this gr...
- In Exercises 107-118, begin by graphing the cube root function, f(x) = âˆ›x. Then use transformations of this gr...