# Lesson 7

Expressing Transformations of Functions Algebraically

- Let’s express transformed 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 \(g\).

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

### Problem 3

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

### 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:

- \(f\) is even
- \(f\) is odd
- \(f\) is neither even nor odd

### 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.

reflection over the \(y\)-axis, then translation up by 2

reflection over the \(x\)-axis, then translation up by 2

translation up 2, then reflection over the \(y\)-axis

translation up 2, then reflection over the \(x\)-axis

translation up 2, and then translation left by 5