Question

q2
when compared to $f(x)=e^x$, how does the graph of $g(x)=3e^{x+2}+4$ differ?
a vertical compression of $\frac{1}{3}$, shifted left 2 units, and shifted down 4 units
b vertical stretch of 3, shifted right 2 units, and shifted down 4 units
c vertical compression of $\frac{1}{3}$, shifted right 2 units, and shifted up 4 units
d vertical stretch of 3, shifted left 2 units, and shifted up 4 units

Explanation:

Step1: Identify vertical transformation

The coefficient of $e^{x+2}$ is 3, so this is a vertical stretch by a factor of 3.

Step2: Identify horizontal shift

The exponent is $x+2$, which is $x - (-2)$, so this is a shift left 2 units.

Step3: Identify vertical shift

The term $+4$ outside the exponential means a shift up 4 units.

Answer:

D. Vertical stretch of 3, shifted left 2 units, and shifted up 4 units