Math Problem Statement
Complete the table and then graph the function.
f
(
x
)
=
–
2
x
x
f
(
x
)
–
4
–
3
–
2
3
4
Solution
Let's start by completing the table for the given function.
The function is:
We will substitute the values of given in the table to find the corresponding values of .
Table Completion:
| -4 | |
| -3 | |
| -2 | |
| 3 | |
| 4 |
So, the completed table looks like:
x & f(x) = -2x \\ \hline -4 & 8 \\ -3 & 6 \\ -2 & 4 \\ 3 & -6 \\ 4 & -8 \\ \end{array}$$ ### Graphing the function: Now, to graph the function $$f(x) = -2x$$, plot the points from the table and draw a straight line passing through them since this is a linear function. 1. Plot the points $$(-4, 8)$$, $$(-3, 6)$$, $$(-2, 4)$$, $$(3, -6)$$, $$(4, -8)$$ on a coordinate plane. 2. Draw a straight line through these points because the function is linear with a slope of -2 (the coefficient of $$x$$). Would you like me to generate a graph for you? --- **Relative questions:** 1. What is the slope of the line represented by $$f(x) = -2x$$? 2. How does the graph of $$f(x) = -2x$$ compare to $$f(x) = x$$? 3. What is the y-intercept of the function $$f(x) = -2x$$? 4. How would the graph change if the function were $$f(x) = 2x$$? 5. Can you explain how negative slopes affect the direction of the line? **Tip:** For linear functions, the slope determines how steep the line is and whether it slants upwards (positive slope) or downwards (negative slope).Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Algebra
Linear Functions
Graphing
Formulas
Linear function formula: f(x) = mx + b
Theorems
Slope-Intercept Form
Suitable Grade Level
Grades 6-8
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