Question

Let f(x)=5x.Let g(x)=5x−7.Which statement describes the graph of g(x)with respect to the graph of f(x)? g(x)is translated 7 units down fromf(x).g(x)is translated 7 units left fromf(x).g(x)is translated 7 units right from f(x).g(x)is translated 7 units up fromf(x).

Answer 1

The graph of g(x) = 5x - 7 is translated 7 units down from the graph of f(x) = 5x, resulting in a vertical shift of the entire graph without any change in slope.

Explanation:

The graph of g(x) = 5x - 7 compared to the graph of f(x) = 5x represents a vertical translation or shift. Since we are subtracting 7 from the function f(x), the graph of g(x) is simply the graph of f(x) moved 7 units downwards. This translation doesn't affect the slope of the line, just its position on the y-axis.

Each point on the graph of g(x) will have the same x-coordinate as the corresponding point on the graph of f(x), but the y-coordinate will be 7 units less.

Answer 2

Given

`\begin{gathered} f(x)=5x \\ g(x)=5x-7 \end{gathered}`

According to rules of transformation:

f(x)+c shift c units up and f(x)-c shift c units down.

For the given function g(x) = 5x-7, 7 is being subtracted from 5x.

Where 5x is represented by f function.

Therefore, we could apply the rules of transformation f(x)-c shift c units down.

Here the value of c is 7.

Answer: g(x) is translated 7 units down from f(x)