Questions: Suppose that G(x)=F(x)-7. Which statement best compares the graph of G(x) with the graph of F(x) ? A. The graph of G(x) is the graph of F(x) shifted 7 units to the left. B. The graph of G'(x) is the graph of F(x) shifted 7 units to the right. C. The graph of G(x) is the graph of F(x) shifted 7 units down. D. The graph of G(x) is the graph of F(x) shifted 7 units up.

Suppose that G(x)=F(x)-7. Which statement best compares the graph of G(x) with the graph of F(x) ?
A. The graph of G(x) is the graph of F(x) shifted 7 units to the left.
B. The graph of G'(x) is the graph of F(x) shifted 7 units to the right.
C. The graph of G(x) is the graph of F(x) shifted 7 units down.
D. The graph of G(x) is the graph of F(x) shifted 7 units up.

Transcript text: Suppose that $G(x)=F(x)-7$. Which statement best compares the graph of $G(x)$ with the graph of $F(x)$ ? A. The graph of $G(x)$ is the graph of $F(x)$ shifted 7 units to the left. B. The graph of $G^{\prime}(x)$ is the graph of $F(x)$ shifted 7 units to the right. C. The graph of $G(x)$ is the graph of $F(x)$ shifted 7 units down. D. The graph of $G(x)$ is the graph of $F(x)$ shifted 7 units up.

Solution

Solution Steps

To compare the graphs of $ G(x) = F(x) - 7 $ and $ F(x) $, we need to understand how subtracting a constant from a function affects its graph. Subtracting a constant from a function results in a vertical shift of the graph. Specifically, subtracting 7 from $ F(x) $ shifts the graph 7 units downward.

Step 1: Understanding the Function Transformation

Given the function $ G(x) = F(x) - 7 $, we need to analyze how this transformation affects the graph of $ F(x) $. The expression indicates that we are subtracting 7 from the output of $ F(x) $.

Step 2: Identifying the Type of Shift

Subtracting a constant from a function results in a vertical shift of the graph. Specifically, if we have $ F(x) $ and we create $ G(x) $ by subtracting 7, the graph of $ G(x) $ will be shifted downward by 7 units. This means that for every point $ (x, F(x)) $ on the graph of $ F(x) $, the corresponding point on the graph of $ G(x) $ will be $ (x, F(x) - 7) $.

Step 3: Comparing the Options

Now, we can compare this transformation to the provided options:

A. The graph of $ G(x) $ is the graph of $ F(x) $ shifted 7 units to the left. (Incorrect)
B. The graph of $ G'(x) $ is the graph of $ F(x) $ shifted 7 units to the right. (Incorrect)
C. The graph of $ G(x) $ is the graph of $ F(x) $ shifted 7 units down. (Correct)
D. The graph of $ G(x) $ is the graph of $ F(x) $ shifted 7 units up. (Incorrect)