Question

Which statement correctly compares the graph of function g with the graph of function f? f ⁡ ( x ) = e x − 4 g ⁡ ( x ) = 1 2 ⁢ e x − 4 A. The graph of function g is a horizontal shift of the graph of function f to the right. B. The graph of function g is a horizontal shift of the graph of function f to the left. C. The graph of function g is a vertical compression of the graph of function f. D. The graph of function g is a vertical stretch of the graph of function f.

Answer 1

Option B is correct

Explanation:

Both the exponential functions f(x) = e(x - 4) and g(x) = (1/2)e(x - 4) have e(x - 4) as their base function. This base function shows a horizontal shift for both functions of 4 units to the right.

We can see that g(x) is produced by multiplying the base function by 1/2 in order to compare the two functions. The graph is vertically compressed as a result of this multiplication, but the horizontal shift is unaffected.

Since the horizontal shift is unchanged, the only difference between the two functions is the vertical compression factor.