The function g(x) is a transformation of f(x). If g(x) has a y-intercept of -2, which of the following functions could represent g(x)? A. g(x) = f(x + 2) B. g(x) = f(x - 5) C. g... The function g(x) is a transformation of f(x). If g(x) has a y-intercept of -2, which of the following functions could represent g(x)? A. g(x) = f(x + 2) B. g(x) = f(x - 5) C. g(x) = f(x) - 5 D. g(x) = f(x) - 2 Read more

Steps to Solve

1. Identify the y-intercept of the original function f(x)

From the graph (which is not provided, but we can assume its y-intercept), let's denote the y-intercept of $f(x)$ as $y_0$.

2. Analyze option A: $f(x) - 2$

This transformation shifts the graph of $f(x)$ downward by 2 units. The new y-intercept will be $y_0 - 2$. We want this to be -2, so we need to check if $y_0 - 2 = -2$. This implies $y_0 = 0$.

3. Analyze option B: $f(x) + 2$

This transformation shifts the graph of $f(x)$ upward by 2 units. The new y-intercept will be $y_0 + 2$. We want this to be -2, so we need to check if $y_0 + 2 = -2$. This implies $y_0 = -4$.

4. Analyze option C: $2f(x)$

This transformation scales the graph of $f(x)$ vertically by a factor of 2. The new y-intercept will be $2y_0$. We want this to be -2, so we need to check if $2y_0 = -2$. This implies $y_0 = -1$.

5. Analyze option D: $-2f(x)$

This transformation scales the graph of $f(x)$ vertically by a factor of -2. The new y-intercept will be $-2y_0$. We want this to be -2, so we need to check if $-2y_0 = -2$. This implies $y_0 = 1$.

6. Need to infer $y_0$ from the context

Since the graph is not provided, we need to determine which of the inferred values of $y_0$ is the most plausible one given the problem context (which is missing).

Let's assume that the y-intercept of the original graph of f(x) is at $y_0 = 0$. Then option A ($f(x) - 2$) would shift the graph down 2 units, resulting in a y-intercept of -2.