Math Problem Statement

Evaluate the function f(x) = 3(-2x + 7) for different values of x: f(-7), f(13), f(11), and f(-8).

Solution

The function provided at the top is:

f(x)=3(2x+7)f(x) = 3(-2x + 7)

Let's evaluate this function at different values of xx as requested:


a) f(7)f(-7):

f(7)=3(2(7)+7)f(-7) = 3(-2(-7) + 7) f(7)=3(14+7)=3×21=63f(-7) = 3(14 + 7) = 3 \times 21 = 63


b) f(13)f(13):

f(13)=3(2(13)+7)f(13) = 3(-2(13) + 7) f(13)=3(26+7)=3×(19)=57f(13) = 3(-26 + 7) = 3 \times (-19) = -57


c) f(11)f(11):

f(11)=3(2(11)+7)f(11) = 3(-2(11) + 7) f(11)=3(22+7)=3×(15)=45f(11) = 3(-22 + 7) = 3 \times (-15) = -45


d) f(8)f(-8):

f(8)=3(2(8)+7)f(-8) = 3(-2(-8) + 7) f(8)=3(16+7)=3×23=69f(-8) = 3(16 + 7) = 3 \times 23 = 69


If you have any questions or need further details, feel free to ask!

Here are five related questions to expand your understanding:

  1. How would you rewrite f(x)f(x) in a simplified form?
  2. What is the slope of the linear function f(x)f(x)?
  3. How does the graph of f(x)f(x) look based on its equation?
  4. What happens to f(x)f(x) as xx becomes very large or very small?
  5. How would you find the x-intercept of f(x)f(x)?

Tip: When evaluating functions, always substitute values for xx carefully, making sure to apply any negative signs properly!

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Functions
Substitution

Formulas

f(x) = 3(-2x + 7)
Substitute x into the function

Theorems

Basic Function Evaluation

Suitable Grade Level

Grades 9-10