Question

graph the exponential function.
$f(x)=3^x$
plot five points on the graph of the function, and also draw the asymptote. then click on the graph - a - function button.

Explanation:

Step1: Choose x-values

Select x-values: -2, -1, 0, 1, 2.

Step2: Calculate f(x) for x=-2

For \( x = -2 \), \( f(-2) = 3^{-2} = \frac{1}{3^2} = \frac{1}{9} \approx 0.11 \).

Step3: Calculate f(x) for x=-1

For \( x = -1 \), \( f(-1) = 3^{-1} = \frac{1}{3} \approx 0.33 \).

Step4: Calculate f(x) for x=0

For \( x = 0 \), \( f(0) = 3^{0} = 1 \).

Step5: Calculate f(x) for x=1

For \( x = 1 \), \( f(1) = 3^{1} = 3 \).

Step6: Calculate f(x) for x=2

For \( x = 2 \), \( f(2) = 3^{2} = 9 \).

Step7: Identify the asymptote

For exponential function \( f(x) = a^x \) (a>0, a≠1), the horizontal asymptote is \( y = 0 \) (since as \( x \to -\infty \), \( 3^x \to 0 \)).

Answer:

Five points: \((-2, \frac{1}{9})\), \((-1, \frac{1}{3})\), \((0, 1)\), \((1, 3)\), \((2, 9)\). Horizontal asymptote: \( y = 0 \). To graph, plot the points and draw a smooth curve approaching \( y = 0 \) as \( x \to -\infty \) and increasing as \( x \to \infty \).