Math Problem Statement

Given the function f(x) = 12x + 3, create a table of values for x ranging from -2 to 2.

Solution

The image contains part of a math problem. The function given is f(x)=12x+3f(x) = 12x + 3, and the task appears to ask for creating a table of values for the function within a specific range, "use -2 to 2."

To solve this:

  1. We will substitute values of xx from -2 to 2 into the function f(x)=12x+3f(x) = 12x + 3.
  2. Calculate the corresponding f(x)f(x) values.

Let's create the table:

  • For x=2x = -2: f(2)=12(2)+3=24+3=21f(-2) = 12(-2) + 3 = -24 + 3 = -21

  • For x=1x = -1: f(1)=12(1)+3=12+3=9f(-1) = 12(-1) + 3 = -12 + 3 = -9

  • For x=0x = 0: f(0)=12(0)+3=0+3=3f(0) = 12(0) + 3 = 0 + 3 = 3

  • For x=1x = 1: f(1)=12(1)+3=12+3=15f(1) = 12(1) + 3 = 12 + 3 = 15

  • For x=2x = 2: f(2)=12(2)+3=24+3=27f(2) = 12(2) + 3 = 24 + 3 = 27

The table of values for f(x)=12x+3f(x) = 12x + 3 over x=2,1,0,1,2x = -2, -1, 0, 1, 2 is:

\hline x & f(x) \\ \hline -2 & -21 \\ -1 & -9 \\ 0 & 3 \\ 1 & 15 \\ 2 & 27 \\ \hline \end{array}$$ Would you like further details or have any questions? ### 5 Related Questions: 1. What happens to the function $$f(x) = 12x + 3$$ as $$x \to \infty$$? 2. How would the table change if the function were $$f(x) = 12x^2 + 3$$? 3. Can you graph the table of values for better visualization? 4. How does the slope of $$f(x) = 12x + 3$$ affect its rate of change? 5. How would the function behave if you shifted the input range to $$x = -3$$ to $$3$$? ### Tip: When creating a table of values, ensure that you use the same step size between consecutive $$x$$-values for a smooth pattern in the function's behavior.

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Math Problem Analysis

Mathematical Concepts

Linear Functions
Algebra

Formulas

f(x) = 12x + 3

Theorems

-

Suitable Grade Level

Grades 6-8