Bush Martin
06/26/2024 · Middle School
In Exercises 9-14, write a function \( g \) whose graph represents 1 Use technology to check your answer. (See Example 2.) 9. \( f(x)=-5 x+2 \) : reflection in the \( x \)-axis
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To solve this problem, we need to find a function \( g(x) \) whose graph is the reflection of the graph of \( f(x) = -5x + 2 \) in the \( x \)-axis.
The reflection of a graph in the \( x \)-axis can be achieved by negating the \( y \)-values of the original function. In other words, if a point \((x, y)\) is on the graph of \( f(x) \), then the point \((x, -y)\) will be on the graph of the reflected function \( g(x) \).
Given \( f(x) = -5x + 2 \), we can find \( g(x) \) by negating the \( y \)-values:
\[ g(x) = -f(x) \]
Substitute \( f(x) \) into the equation:
\[ g(x) = -(-5x + 2) \]
Now, simplify the expression:
\[ g(x) = 5x - 2 \]
So, the function \( g(x) \) whose graph represents the reflection of \( f(x) = -5x + 2 \) in the \( x \)-axis is:
\[ g(x) = 5x - 2 \]
To check this answer using technology, you can plot the graph of \( f(x) = -5x + 2 \) and the graph of \( g(x) = 5x - 2 \) on the same coordinate plane. You should see that the graph of \( g(x) \) is the reflection of the graph of \( f(x) \) in the \( x \)-axis.
Quick Answer
The function \( g(x) \) is \( g(x) = 5x - 2 \).
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