Function Operations

​EVALUATING FUNCTIONS

​Dr. Tom Giles

​EVALUATING FUNCTIONS

Evaluating a function involves determining the value of the function that corresponds to a specific value of x. Simply substituting x with the given value will do. Our learning targets for today’s discussion are as follows:

​

1. I can recall how to evaluate functions; and

2. I can evaluate functions graphically.

​

​ESSENTIAL QUESTION

​How can we use function notation to evaluate a function?

​

SUMMARY​

To evaluate a function, substitute the input (the given number or expression) for the function's variable (place holder, x). Replace the x with the number or expression, then follow the order of operations​

​LET'S TRY! :)

Multiple Choice

Given that f(x) = 3x + 6, find f(-2).

• 2

• -1

• 0

• 1

Multiple Choice

Given that g(x) = x²  - 5x -12, find g(-5).

• 38

• 18

• 15

• 0

Multiple Choice

Find 4h(3), given that h(x) = $$\frac{x+6}{2}$$  

• 8

• 18

• 15

• 0

Multiple Choice

Given that f(x) = 5 - 2x and g(x) = 5x + 12, find 2f(0) - 3g(-2).

• 6

• 4

• -6

• -4

Multiple Choice

Given that j(x) = 3x -10, what is x if j(x) = 20.

• -5

• 8

• -6

• 10

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SUMMARY​

The graph of a function is a way of viewing the outputs of the function for all possible inputs. Here, we let y=f(x) so that each y-value represents the output and each x-value represents the input. This means any point on the graph is: (x,y)=(input,corresponding output)

​LET'S TRY! :)

Multiple Choice

Given the graph of f. Find f(-1)

• 0

• -1

• 1

• 2

Multiple Choice

Given the graph of f. Find f(2)

• 3

• 2

• 1

• 0

Multiple Choice

Given the graph of f. Find 3f(-2) + 5f(1)

• -15

• 16

• 17

• -17

Multiple Choice

Given the graph of f. Find f(x) = 0

• 3

• 2

• -1

• 0

Multiple Choice

Given the graph of f. Find f(x) = 1

• (-1, 1)

• {-1, 1)

• (-1, 1}

• {-1, 1}

​

Let's summarize

The graph of a function is a way of viewing the outputs of the function for all possible inputs. Here, we let y=f(x) so that each y-value represents the output and each x-value represents the input. This means any point on the graph is: (x,y)=(input,corresponding output)

To evaluate a function, substitute the input (the given number or expression) for the function's variable (place holder, x). Replace the x with the number or expression, then follow the order of operations​

​Function

​Graph of a Function