I want to understand functions and know how to plot graphs

Question

ScanSolve AI Tutor · Accepted Answer

A function is a rule that assigns to each input value exactly one output value. We often write functions as f(x), where 'x' is the input and 'f(x)' is the output. To plot a graph of a function, you follow these steps: 1. Create a table of values: Choose several input values for 'x' (e.g., −2, −1, 0, 1, 2). 2. Calculate the output: For each 'x' value, calculate the corresponding 'f(x)' value using the function's rule. 3. Plot the points: Treat each (x, f(x)) pair as coordinates on a graph. The 'x' value is the horizontal position, and the 'f(x)' value is the vertical position. 4. Draw the curve: Connect the plotted points with a smooth line or curve. If the function is continuous, the line should be unbroken. For example, let's plot the function f(x) = 2x + 1. Step 1: Create a table of values. x | f(x) = 2x + 1 --|-------------- −2| −1| 0 | 1 | 2 | Step 2: Calculate the output. x | f(x) = 2x + 1 --|-------------- −2| 2(−2) + 1 = −3; −1| 2(−1) + 1 = −1; 0 | 2(0) + 1 = 1; 1 | 2(1) + 1 = 3; 2 | 2(2) + 1 = 5 Step 3: Plot the points. The points are (−2, −3), (−1, −1), (0, 1), (1, 3), and (2, 5). Step 4: Draw the curve. Connecting these points forms a straight line.

Point	x	y
x-intercept	−0.5	0
y-intercept	0	1

I want to understand functions and know how to plot graphs

Answer

Step-by-step solution

Create a table of values.

Calculate the output.

Plot the points.

Draw the curve.

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