f(x) = 8 · 1.2^x

Understand the Problem

The question appears to involve graphing an exponential function, specifically f(x) = 8 · 1.2^x, on a grid provided. The task likely requires plotting points and analyzing the behavior of the function.

Answer

Plot points for $f(x) = 8 \cdot 1.2^x$: $(-2, 5.56)$, $(-1, 6.67)$, $(0, 8)$, $(1, 9.6)$, $(2, 11.52)$.

Steps to Solve

Choose x-values to evaluate

Start by selecting a range of $x$-values that will provide a good representation of the function. Common values to choose are negative, zero, and positive values. For example, let's use: $-2, -1, 0, 1, 2$.

Calculate corresponding f(x) values

Next, calculate $f(x)$ for each chosen $x$-value using the function $f(x) = 8 \cdot 1.2^x$.

For $x = -2$: $$ f(-2) = 8 \cdot 1.2^{-2} = 8 \cdot \frac{1}{1.44} \approx 5.56 $$
For $x = -1$: $$ f(-1) = 8 \cdot 1.2^{-1} = 8 \cdot \frac{1}{1.2} \approx 6.67 $$
For $x = 0$: $$ f(0) = 8 \cdot 1.2^0 = 8 \cdot 1 = 8 $$
For $x = 1$: $$ f(1) = 8 \cdot 1.2^{1} = 8 \cdot 1.2 = 9.6 $$
For $x = 2$: $$ f(2) = 8 \cdot 1.2^{2} = 8 \cdot 1.44 \approx 11.52 $$

Plot the points on a grid

Now, plot the points you calculated:

$(-2, 5.56)$
$(-1, 6.67)$
$(0, 8)$
$(1, 9.6)$
$(2, 11.52)$

Place each point on the grid according to its coordinates.

Draw the curve

After plotting all the points, draw a smooth curve that connects them. This curve will represent the exponential function, showing its growth as $x$ increases.

The plotted points for the function $f(x) = 8 \cdot 1.2^x$ are:

$(-2, 5.56)$
$(-1, 6.67)$
$(0, 8)$
$(1, 9.6)$
$(2, 11.52)$

More Information

Exponential functions like $f(x) = 8 \cdot 1.2^x$ exhibit rapidly increasing growth for positive $x$ values. This particular function starts at a value of $8$ when $x = 0$, and as $x$ increases, the output grows larger, demonstrating the nature of exponential growth.

Tips

Incorrect calculations: Ensure to carefully compute each value of $f(x)$, especially the powers and multiplication.
Plotting errors: Double-check the coordinates on the grid to avoid misplacing points.

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