Math Problem Statement

Patrick is practicing evaluating functions. He is using the following functions.  

f(x) = −6 + 14x  g(x) = (2x + 9)2  

He evaluates the functions for f(7) and g(−3). What values will he calculate?

Select TWO correct answers.

Solution

Let's evaluate the functions f(x)f(x) and g(x)g(x) for the given values x=7x = 7 and x=3x = -3.

Function f(x)=6+14xf(x) = -6 + 14x

Evaluate f(7)f(7):

f(7)=6+14(7)f(7) = -6 + 14(7)

f(7)=6+98f(7) = -6 + 98

f(7)=92f(7) = 92

Function g(x)=(2x+9)2g(x) = (2x + 9)^2

Evaluate g(3)g(-3):

g(3)=(2(3)+9)2g(-3) = (2(-3) + 9)^2

g(3)=(6+9)2g(-3) = (-6 + 9)^2

g(3)=32g(-3) = 3^2

g(3)=9g(-3) = 9

Final Answer

The values that Patrick will calculate are:

  • f(7)=92f(7) = 92
  • g(3)=9g(-3) = 9

So the correct answers are 92\boxed{92} and 9\boxed{9}.

Would you like more details, or do you have any other questions?

Relative Questions:

  1. How do you evaluate functions for specific values of xx?
  2. What is the general form of a linear function?
  3. How do you expand and simplify squared binomials like (2x+9)2(2x + 9)^2?
  4. What happens if the input to a function is a fraction or a decimal?
  5. Can we evaluate these functions graphically using a graphing calculator?

Tip:

Always substitute the given value of xx carefully and follow the order of operations (PEMDAS) when evaluating functions.

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Math Problem Analysis

Mathematical Concepts

Functions
Evaluation of Functions
Quadratic Equations

Formulas

Function evaluation
Square of a binomial

Theorems

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Suitable Grade Level

Grades 9-10