Question

Simplify the function f(x) = 7(8x² - 9). Then answer the questions below:

The initial value for the function is:
A) 7
B) 0
C) -9
D) -63

Answer 1

To simplify the function f(x) = 7(8x² - 9), we multiply each term inside the parentheses by 7, resulting in f(x) = 56x² - 63. The initial value of the function is found by evaluating f(0), which results in -63. Therefore, the initial value is -63 (option D).

Step-by-step explanation:

To simplify the function f(x) = 7(8x² - 9), we distribute the 7 to both terms inside the parentheses:

f(x) = 7 × 8x² - 7 × 9

This simplifies to:

f(x) = 56x² - 63

The initial value for the function is the y-intercept, which is the value of the function when x = 0:

f(0) = 56(0)² - 63 = -63

Therefore, the initial value is D) -63.

To check if this answer is reasonable, you can see that when x=0, the term containing x (56x²) becomes zero, and only the constant term (-63) remains. This confirms that the initial value of the function (its y-intercept) is indeed -63.