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.
The equation of the curve is f left parenthesis x right parenthesis equals negative 3 superscript x baseline minus 2. The coordinates through which the curve passes through are left parenthesis negative 10 comma negative 2 right parenthesis, left parenthesis negative 3 comma negative 2 right parenthesis, left parenthesis 0 comma negative 3 right parenthesis, left parenthesis 1 comma negative 5 right parenthesis, and left parenthesis 2 comma negative 10 right parenthesis. Points are approximate.


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

(1 point)
The range of the function is y [?] .

Answer 1

y < -2

Reason: 3^x > 0 for all x, so -3^x - 2 < -2, and as x → -∞ the expression approaches -2 but never reaches it. Hence the range is (-∞, -2).