Question

use the drawing tools to form the correct answer on the graph.

plot points to create a graph of (y = f(x)) on the domain (\\{0, 1, 2, 3\\}).

(f(x) = 2^x - 7)

Explanation:

🆕 New Concept Discovered: Graphing Exponential Functions
Plotting discrete points of an exponential curve

Step 1: Understand the domain and function

The function is:

$$ f(x) = 2^x - 7 $$

The domain is given as a discrete set of values:

$$ \{0, 1, 2, 3\} $$

This means we only calculate and plot points for these specific \( x \)-values.

Step 2: Calculate the points

We substitute each \( x \)-value from the domain into the function to find its corresponding \( y \)-value:

• For \( x = 0 \):

$$ f(0) = 2^0 - 7 = 1 - 7 = -6 $$

Point: \( (0, -6) \)

• For \( x = 1 \):

$$ f(1) = 2^1 - 7 = 2 - 7 = -5 $$

Point: \( (1, -5) \)

• For \( x = 2 \):

$$ f(2) = 2^2 - 7 = 4 - 7 = -3 $$

Point: \( (2, -3) \)

• For \( x = 3 \):

$$ f(3) = 2^3 - 7 = 8 - 7 = 1 $$

Point: \( (3, 1) \)

Step 3: Plot the points on the coordinate plane

Using the point tool, plot the following four discrete points on the graph:

1. \( (0, -6) \)
2. \( (1, -5) \)
3. \( (2, -3) \)
4. \( (3, 1) \)

Do not connect the points with a line or curve, because the domain is restricted to only the discrete set \( \{0, 1, 2, 3\} \).

Answer:

The points to plot on the graph are:

• \( (0, -6) \)
• \( (1, -5) \)
• \( (2, -3) \)
• \( (3, 1) \)