Question

1
select the correct answer.
what is the y-intercept of $f(x) = 3^{x + 2}$?
a. (9,0)
b. (0,9)
c. (0,-9)
d. (9,-9)

Explanation:

Step1: Recall y - intercept definition

The y - intercept of a function \(y = f(x)\) is the point where \(x = 0\). So we need to find \(f(0)\) for the function \(f(x)=3^{x + 2}\).

Step2: Substitute \(x = 0\) into the function

Substitute \(x = 0\) into \(f(x)=3^{x+2}\), we get \(f(0)=3^{0 + 2}\).

Step3: Simplify the exponent

Simplify the exponent: \(0+2 = 2\), so \(f(0)=3^{2}\).

Step4: Calculate \(3^{2}\)

We know that \(3^{2}=3\times3 = 9\). So when \(x = 0\), \(y=f(0) = 9\), and the y - intercept is the point \((0,9)\).

Answer:

B. \((0,9)\)