Question

The linear parent function, A(x) = x, is transformed to g(x) = 2x + 7. Which statement correctly compares the graphs of the functions?

A. The graph of g(x) is less steep than the graph of f(x) and the y intercept has been shifted up.
B. The graph of g(x) is steeper than the graph of f(x) and the y intercept has been shifted up.
C. The graph of g(x) is less steep than the graph of f(x) and the y intercept has been shifted down.
D. The graph of g(x) is steeper than the graph of f(x) and they intercept has been shifted down.

Answer 1

The function g(x) = 2x + 7 has a steeper slope than the linear parent function A(x) = x, and its y-intercept has been shifted up from 0 to 7.

Step-by-step explanation:

The student is asking about the transformation of the linear parent function A(x) = x to a new function g(x) = 2x + 7. When comparing these two functions, we're looking at the changes in slope and y-intercept. The slope of the linear parent function A(x) is 1 (rise over run of 1/1), while for g(x), the slope is 2, indicating a rise of 2 for every increase of 1 on the horizontal axis. This means that g(x) is indeed steeper than A(x). Regarding the y-intercept, A(x) intersects the y-axis at 0, and g(x) intersects the y-axis at 7, which is a shift upwards. Therefore, the correct statement that compares the graphs of the two functions is B: The graph of g(x) is steeper than the graph of A(x) and the y-intercept has been shifted up.