Question

a) 10
b) 7
c) 5
d) 4
question 12 (1 point)
the x-intercept of the function $y = -4\log(x + 3)$ is
a) -4
b) 3
c) -2
d) -3

Explanation:

Step1: Recall x-intercept definition

At x-intercept, \( y = 0 \). So set \( y = 0 \) in \( y=-4\log(x + 3) \).
\( 0=-4\log(x + 3) \)

Step2: Solve for \( x \)

Divide both sides by -4: \( \frac{0}{-4}=\log(x + 3) \) → \( 0=\log(x + 3) \).
Assuming base 10 (common log), \( \log_{10}(x + 3)=0 \) means \( x + 3 = 10^0 \) (since \( \log_b a = c \) ⇨ \( a = b^c \)).
\( 10^0 = 1 \), so \( x + 3 = 1 \) → \( x = 1 - 3=-2 \).

Answer:

c) -2