f
(
x
)
=
2
x
−
3
The function f(x) = 2x - 3 represents a linear equation. It takes an input x, multiplies it by 2, and then subtracts 3 from the result.
To graph the function f(x) = 2x - 3, follow these steps:
Step 1: Choose x-values
Choose a few values for x to find the corresponding y-values. It's usually helpful to pick values that are easy to calculate. Let's choose three x-values: x = -1, 0, and 1.
Step 2: Calculate y-values
Substitute the chosen x-values into the function to find the corresponding y-values. Use the equation f(x) = 2x - 3.
For x = -1,
f(-1) = 2(-1) - 3 = -2 - 3 = -5
For x = 0,
f(0) = 2(0) - 3 = 0 - 3 = -3
For x = 1,
f(1) = 2(1) - 3 = 2 - 3 = -1
Step 3: Plot the points
Plot the points (-1, -5), (0, -3), and (1, -1) on a coordinate plane. These represent the chosen x-values and their corresponding y-values.
Step 4: Draw a line
Draw a straight line through the plotted points. The line will extend infinitely in both directions. This line represents the graph of the function f(x) = 2x - 3.
Note: The line has a positive slope of 2, which means the function increases as x increases. The y-intercept is -3, which is the value of y when x = 0.