Question

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

Explanation:

Step1: Choose x-values, solve for f(x)

Select \(x = -2, -1, 0, 1, 2\):

• \(x=-2\): \(f(-2)=3^{-2}=\frac{1}{9}\approx0.11\)
• \(x=-1\): \(f(-1)=3^{-1}=\frac{1}{3}\approx0.33\)
• \(x=0\): \(f(0)=3^{0}=1\)
• \(x=1\): \(f(1)=3^{1}=3\)
• \(x=2\): \(f(2)=3^{2}=9\)

Step2: List coordinate points

The points are:
\((-2, \frac{1}{9})\), \((-1, \frac{1}{3})\), \((0, 1)\), \((1, 3)\), \((2, 9)\)

Step3: Plot points, draw curve

Plot each point on the grid, then draw a smooth increasing curve through them, approaching the x-axis as \(x\to-\infty\).

Answer:

The five points to plot are \(\boldsymbol{(-2, \frac{1}{9})}\), \(\boldsymbol{(-1, \frac{1}{3})}\), \(\boldsymbol{(0, 1)}\), \(\boldsymbol{(1, 3)}\), and \(\boldsymbol{(2, 9)}\). Connect these points with a smooth, upward-sloping curve that approaches the x-axis as x decreases toward negative infinity.