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Exercises 9.8 Practice Problems

1.

Below is the graph of \(f(x)\text{.}\)

What does the graph of \(g(x)\) look like if \(g(x)=f(x)+2\text{?}\)

2.

Below is the graph of \(f(x)\text{.}\)

What does the graph of \(g(x)\) look like if \(g(x)=f(x)-3\text{?}\)

3.

Below is the graph of \(f(x)\text{.}\)

What does the graph of \(g(x)\) look like if \(g(x)=f(x)+5\text{?}\)

4.

Suppose the solid blue graph below is the graph of \(f(x)\) and the red graph is the graph of \(g(x)\text{:}\)

Write a formula for \(g(x)\) in terms of \(f(x)\text{.}\)

Answer.

\(g(x)=f(x)-4\)

5.

Suppose the solid blue graph below is the graph of \(f(x)\) and the red graph is the graph of \(g(x)\text{:}\)

Write a formula for \(g(x)\) in terms of \(f(x)\text{.}\)

Answer.

\(g(x)=f(x)+3\)

6.

Suppose \(f(x)=x^3-2x+1\) and \(g(x)\) is the same as \(f(x)\) but shifted down by \(3\text{.}\) Write a formula for \(g(x)\text{.}\)

Answer.

\(g(x)=x^3-2x-2\)

7.

Suppose \(f(x)=3x^2\) and \(g(x)=3x^2-4\text{.}\) What transformations took \(f(x)\) to \(g(x)\text{?}\)

Answer.

Shift down by \(4\text{.}\)

8.

Suppose \(f(x)=x^2-3\) and \(g(x)\) is the same as \(f(x)\) but shifted up by \(1\text{.}\) Write a formula for \(g(x)\text{.}\)

Answer.

\(g(x)=x^2-2\)

9.

Suppose \(f(x)=3x+4\) and \(g(x)=3x+8\text{.}\) What transformations took \(f(x)\) to \(g(x)\text{?}\)

Answer.

Shift up by \(4\text{.}\)