Question

question 9 (multiple choice worth 8 points)
(graphing of exponential functions lc)

graph the exponential function represented in the table.

\\(\

$$\begin{array}{|c|c|c|c|c|}\\hline x & -1 & 0 & 1 & 2 \\\\\\hline h(x) & 0.8 & 2 & 5 & 12.5 \\\\\\hline\\end{array}$$

\\)

Explanation:

Find the base and initial value

$$
LATEXBLOCK0
$$

Write the exponential function

$$ h(x) = 2 \cdot (2.5)^x $$

Verify with remaining points

$$
LATEXBLOCK1
$$

Answer:

The exponential function represented by the table is \(h(x) = 2 \cdot (2.5)^x\).

To graph this function, plot the key points from the table:

• \((-1, 0.8)\)
• \((0, 2)\) (y-intercept)
• \((1, 5)\)
• \((2, 12.5)\)

Draw a smooth, continuously increasing curve passing through these points, with a horizontal asymptote at the x-axis (\(y = 0\)) as \(x \to -\infty\).