Math Problem Statement

Use the function rule to complete the table. The output (y) is 2 less than 4 times the input (x).

Solution

The problem states that the output yy is "2 less than 4 times xx." This can be written as the function:

y=4x2y = 4x - 2

Using this function, let's calculate yy for each input xx in the table:

  1. For x=1x = -1: y=4(1)2=42=6y = 4(-1) - 2 = -4 - 2 = -6

  2. For x=0x = 0: y=4(0)2=02=2y = 4(0) - 2 = 0 - 2 = -2

  3. For x=1x = 1: y=4(1)2=42=2y = 4(1) - 2 = 4 - 2 = 2

  4. For x=2x = 2: y=4(2)2=82=6y = 4(2) - 2 = 8 - 2 = 6

Now, we can complete the table:

\hline \text{Input } (x) & \text{Output } (y) \\ \hline -1 & -6 \\ 0 & -2 \\ 1 & 2 \\ 2 & 6 \\ \hline \end{array}$$ Would you like further details on how the function rule works, or have any questions? Here are some related questions to deepen your understanding: 1. What would the output be if $$x = 3$$? 2. How would the function change if it was "3 less than 5 times $$x$$"? 3. Can you identify the slope and y-intercept of the function $$y = 4x - 2$$? 4. How does the output change as $$x$$ increases by 1? 5. What if the function rule was instead "4 times $$x$$ less 2"? **Tip:** When working with function rules, always substitute the given input values carefully to calculate the output accurately.

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Math Problem Analysis

Mathematical Concepts

Algebra
Functions
Linear Equations

Formulas

y = 4x - 2

Theorems

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Suitable Grade Level

Grades 6-8