Question

graph the function \\(a(x) = -3(1.7)^x\\).

Explanation:

Identify the horizontal asymptote

Using the Horizontal Asymptotes knowledge point

$$ y = 0 $$

Calculate key coordinate points

Using the Graphing Exponential Functions knowledge point

$$
LATEXBLOCK0
$$

Analyze the function behavior

Using the Graphing Exponential Functions knowledge point

$$
LATEXBLOCK1
$$

Answer:

To graph the function \(a(x) = -3(1.7)^x\), plot the horizontal asymptote and key points:

1. Horizontal Asymptote:

\(y = 0\) (the x-axis) as \(x \to -\infty\).

1. Key Points:

• \(y\)-intercept: \((0, -3)\)
• Additional point: \((1, -5.1)\)
• Additional point: \((-1, -1.76)\)

1. Shape:

The graph starts near the x-axis on the left and curves downwards rapidly to the right.