Math Problem Statement

The function h is defined by the rule h(x) = 4x + 4. Complete the function table for given x values: -3, -1, 0, 3, 5.

Solution

The given function is h(x)=4x+4h(x) = 4x + 4. We need to complete the function table by calculating h(x)h(x) for each given value of xx.

Calculations:

  1. For x=3x = -3: h(3)=4(3)+4=12+4=8h(-3) = 4(-3) + 4 = -12 + 4 = -8
  2. For x=1x = -1: h(1)=4(1)+4=4+4=0h(-1) = 4(-1) + 4 = -4 + 4 = 0
  3. For x=0x = 0: h(0)=4(0)+4=0+4=4h(0) = 4(0) + 4 = 0 + 4 = 4
  4. For x=3x = 3: h(3)=4(3)+4=12+4=16h(3) = 4(3) + 4 = 12 + 4 = 16
  5. For x=5x = 5: h(5)=4(5)+4=20+4=24h(5) = 4(5) + 4 = 20 + 4 = 24

Completed Function Table:

xxh(x)h(x)
-3-8
-10
04
316
524

Would you like further details or have any questions?

Related Questions:

  1. How do you determine the slope of a linear function like h(x)=4x+4h(x) = 4x + 4?
  2. What is the y-intercept of the function h(x)=4x+4h(x) = 4x + 4?
  3. How do you graph the function h(x)=4x+4h(x) = 4x + 4 using the table values?
  4. What happens to the value of h(x)h(x) as xx increases?
  5. How would the function table change if the function was h(x)=4x4h(x) = 4x - 4?

Tip:

For any linear function of the form h(x)=mx+bh(x) = mx + b, mm represents the slope, indicating how steep the line is, and bb is the y-intercept, showing where the line crosses the y-axis.

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Math Problem Analysis

Mathematical Concepts

Linear Functions
Function Evaluation
Algebra

Formulas

h(x) = 4x + 4

Theorems

Definition of a Linear Function

Suitable Grade Level

Grades 6-8