# Lesson 7

Expressing Transformations of Functions Algebraically

### Problem 1

Here is a graph of $$f(x)=e^x$$ and a graph of $$g$$, which is a transformation of $$f$$. Write an equation for the function $$g$$.

### Problem 2

Describe the transformation that takes the graph of function $$f$$ to the graph of function $$g$$.

1. $$f(x)=e^x$$ and $$g(x)=\text-e^x+2.7$$
2. $$f(x)=x^5$$ and $$g(x)=(\text-x+3.1)^5+1$$
3. $$f(x)=|x|$$ and $$g(x)=|x|-26$$
4. $$f(x)=\sqrt x$$ and $$g(x)=\text-\sqrt{x-0.004}$$

### Problem 3

1. Write an equation whose graph is a parabola with vertex at $$(1,4)$$ and which opens upward.
2. Write an equation whose graph is a parabola with vertex at $$(2,\text-3)$$ and which opens downward.

### Problem 4

Describe how to move the graph so that it better matches the data.

### Solution

(From Unit 5, Lesson 1.)

### Problem 5

Here is a graph of $$y = f(x)$$ for $$\text-10 \le x \le 0$$. Sketch $$f$$ for $$0 \le x \le 10$$ if:

1. $$f$$ is even
2. $$f$$ is odd
3. $$f$$ is neither even nor odd

### Solution

(From Unit 5, Lesson 6.)

### Problem 6

Here are graphs of functions $$f$$ and $$g$$.

Which sequences of transformations take the graph of $$f$$ to the graph of $$g$$? Select all that apply.

A:

reflection over the $$y$$-axis, then translation up by 2

B:

reflection over the $$x$$-axis, then translation up by 2

C:

translation up 2, then reflection over the $$y$$-axis

D:

translation up 2, then reflection over the $$x$$-axis

E:

translation up 2, and then translation left by 5