Graph the function f ( x )

To graph the function $f(x) = 4x + 2$, we will start by plotting key points. This is a linear function, which means the graph will be a straight line. The general form of a linear function is $f(x) = mx + b$, where:

• $m$ is the slope
• $b$ is the y-intercept

For $f(x) = 4x + 2$:

• The slope $m = 4$, meaning the line rises 4 units for every 1 unit it moves to the right.
• The y-intercept $b = 2$, which means the line crosses the y-axis at $(0, 2)$.

Key Steps for Graphing:

1. Plot the y-intercept: The line crosses the y-axis at $(0, 2)$.
2. Use the slope: Starting at $(0, 2)$, use the slope of 4 to find another point. From $(0, 2)$, move up 4 units and 1 unit to the right, landing on $(1, 6)$.
3. Draw the line: Connect these points and extend the line in both directions.

Key Points:

• $(0, 2)$
• $(1, 6)$
• $(-1, -2)$ (Moving left from the y-intercept: down 4 units and 1 unit to the left)

This gives you a straight line that can be plotted on the graph.

Would you like me to generate a graph for you or need further details on the process?

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Here are 5 related questions you might find interesting:

1. What is the slope of the line for the equation $f(x) = 4x + 2$?
2. How do you graph a line given its slope and y-intercept?
3. How would you graph the equation $f(x) = -2x + 3$?
4. What happens to the graph if the slope changes to 0?
5. How do you find the x-intercept of the line $f(x) = 4x + 2$?

Tip: Always start graphing linear equations by plotting the y-intercept first and then use the slope to find another point.