Question

question
find the y - intercept and equation of the horizontal asymptote of the function ( f(x)=-4 e^{x}-7 ). round to the the nearest two decimal places as needed.
provide your answer below:
y - intercept: ( (0,-11) ) write as an ordered pair.
horizontal asymptote: write as an equation.

Explanation:

Step1: Find the y - intercept

The y - intercept occurs when \(x = 0\). Substitute \(x=0\) into the function \(f(x)=-4e^{x}-7\).

$$
LATEXBLOCK0
$$

So the y - intercept is the point \((0,-11)\).

Step2: Find the horizontal asymptote

For the exponential function \(y = ae^{x}+b\), when \(x\to-\infty\), \(e^{x}\to0\).
As \(x\to-\infty\), \(f(x)=-4e^{x}-7\to - 7\)

Answer:

• \(y\) - intercept: \((0,-11)\)
• Horizontal Asymptote: \(y=-7\)