Question

Use the image to answer the question.

A curve with arrows at both the ends facing downward is plotted on a coordinate plane with x and y axes ranging from negative 10 to 10 in unit increments.

An exponential function has the equation f(x)=−3x−2
. Complete the inequality to show the range of the function.

(1 point)
The range of the function is y

.

Answer 1

To find the range of the exponential function \( f(x) = -3x - 2 \), we need to analyze its behavior.

The function is a linear function, not an exponential function, and its expression shows that it has a negative slope. This means it will continue to decrease as \( x \) increases. Specifically:

1. As \( x \) approaches positive infinity (\( x \to +\infty \)), the value of \( f(x) \) will approach negative infinity (\( f(x) \to -\infty \)).
2. As \( x \) approaches negative infinity (\( x \to -\infty \)), the value of \( f(x) \) will approach positive infinity (\( f(x) \to +\infty \)).

Given these observations, the vertical placement of the function suggests it does not have a maximum value (it can rise indefinitely) and has no lower bound (it can decrease indefinitely).

Thus, we can express the range of the function \( f(x) = -3x - 2 \) as:

The range of the function is \( y \in (-\infty, \infty) \) or simply \( y \) can take any real number value.

So to complete the inequality,

**The range of the function is** \( y \in (-\infty, \infty) \) **or** \( y \) is any real number.