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College Algebra

Exercises 9.4 Practice Problems

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 \(g(x)\text{.}\)
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Answer.
\(g(x)=x^3-2x-2\)
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10.

Suppose the domain of a function \(f(x)\) is \(\left[1,5\right)\) and its range is \(\left[-1,4\right]\text{.}\) What is the domain and range of the function \(g(x)=f(x+2)-3\text{?}\)
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Answer.
The domain of \(g(x)\) is \(\left[-1,3\right)\) and its range is \(\left[-4,1\right]\text{.}\)
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11.

Suppose the domain of a function \(f(x)\) is \(\left[0,10\right)\) and its range is \(\left[-10,2\right]\text{.}\) What is the domain and range of the function \(g(x)=-2f(x)\text{?}\)
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Answer.
The domain of \(g(x)\) is \(\left[0,10\right)\) and its range is \(\left[-4,20\right]\text{.}\)
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12.

Suppose the domain of a function \(f(x)\) is \(\left[-2,7\right)\) and its range is \(\left[0,8\right]\text{.}\) What is the domain and range of the function \(g(x)=f(-x)+1\text{?}\)
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Answer.
The domain of \(g(x)\) is \(\left(-7,2\right]\) and its range is \(\left[1,9\right]\text{.}\)
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13.

Suppose the domain of a function \(f(x)\) is \(\left[-7,8\right)\) and its range is \(\left[3,12\right]\text{.}\) What is the domain and range of the function \(g(x)=f(2x)-1\text{?}\)
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Answer.
The domain of \(g(x)\) is \(\left[-\frac{7}{2},4\right)\) and its range is \(\left[2,11\right]\text{.}\)
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14.

Suppose \(g(x)=2f(x-3)\text{.}\) What transformations took \(f(x)\) to \(g(x)\text{?}\)
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Answer.
There is a vertical stretch by 2 and a horizontal shift right by 3.
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16.

Suppose \(g(x)=-f(x+1)\text{.}\) What transformations took \(f(x)\) to \(g(x)\text{?}\)
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Answer.
There is a vertical flip and a horizontal shift left by 1.
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17.

Suppose \(g(x)=f(\frac{1}{2}x)-4\text{.}\) What transformations took \(f(x)\) to \(g(x)\text{?}\)
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Answer.
There is a horizontal stretch by 2 and a vertical shift down by 4.
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18.

Suppose \(g(x)=f(x-8)+6\text{.}\) What transformations took \(f(x)\) to \(g(x)\text{?}\)
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Answer.
There is a vertical shift up by 6 and a horizontal shift right by 8.
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19.

Suppose the blue graph below is the graph of \(f(x)\) and the red graph is the graph of \(g(x)\text{:}\)
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Write a formula for \(g(x)\) in terms of \(f(x)\text{.}\)
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Answer.
\(g(x)=f\left(-x\right)+1\)
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20.

Suppose the blue graph below is the graph of \(f(x)\) and the red graph is the graph of \(g(x)\text{:}\)
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Write a formula for \(g(x)\) in terms of \(f(x)\text{.}\)
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Answer.
\(g(x)=-f\left(x+4\right)\)
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21.

Suppose the blue graph below is the graph of \(f(x)\) and the red graph is the graph of \(g(x)\text{:}\)
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Write a formula for \(g(x)\) in terms of \(f(x)\text{.}\)
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Answer.
\(g(x)=-f\left(\frac{1}{2}x\right)\)
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22.

Suppose the blue graph below is the graph of \(f(x)\) and the red graph is the graph of \(g(x)\text{:}\)
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Write a formula for \(g(x)\) in terms of \(f(x)\text{.}\)
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Answer.
\(g(x)=f\left(-x\right)+2\)
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