Chapter 17 Evaluating Functions

Question 2

17-4 (16 already covered and 17-1 through 17-3)

Define a function

Answer 2

A function is a relationship that maps inputs to exactly one output each.
Inputs are domains. (also known as x) They are independent.
Outputs are range (also known as y values.) They are dependent.
Remember each x can have only one y in a function

Question 3

17-4

Know what is special about a linear function.

Answer 3

There are no powers greater than 1 and it graphs to a straight line.

Question 4

17-4

Define the difference between a monomial function and a polynomial function.

Answer 4

Monomial has only one term.
Polynomial has at least two terms added or subtracted together.

Question 5

17-4

Define constants, variables, and coefficients.

Answer 5

• Constant is a number
• Variable is a letter representing an unknown
• Coefficients are variables and a number together. Usually the number is written first.

Question 6

17-4

Define a rational function.

Answer 6

A rational function is a ratio of two polynomials.

Question 7

17-4

Define a constant function.

Answer 7

A constant function gives the same output for every input. There are no variables, only constants (numbers)

Question: If a function is a relationship that maps inputs to exactly one output each, How is that different from a constant function?

Question 8

17-4

explain the difference between a one-to-one function, a many-one function, and a constant function.

Answer 8

A constant function always has the same value for y.
A one-to-one function has a different value for each y.
A many-one function means that the output can be obtained in more that one way.

Constant function example: f(x) = 5
One-to-one- function example: f(x) = 3x
Many-one example: f(x) = x²

Question 9

17-4

How to read or say f(x) =

Answer 9

Say, “f of x equals”

Question 10

17-4

Solve. Given f(x) = 3x + 7
What is f(3)?

Answer 10

Substitute 3 for the x value and solve.
3(3) + 7 =16

Question 11

17-4

How to find the domain of a function. This means what are the x’s that will solve the function. (Remember: your answer can never include the possibility of dividing by 0 or taking the square root of a negative number.)

Answer 11

• If there is a denominator, determine what numbers would make it equal 0. These numbers will be excluded.
• Solve the equation.

Question 12

17-4

do the ordered pair or the input-output test to see if something is a function.

Answer 12

If any x value is paired with two or more y values, it is not a function.

Question 13

17-5

do the vertical line test to see if something is a function

Answer 13

• Imagine a vertical line through a graph
• If the line hits the graph more than once, it is not a function.

Question 14

17-6 and 17-7 and 17-8

solve composite functions

Answer 14

Work from the inside parenthesese out. Once you solve the inside, substitue that answer into the outer function. Continue until everything is solved.

Question 15

17-9, 17-10, 17-11, 17-12

list the three forms of quatratic functions

Answer 15

Question 16

17-12

know what does the r and s stand for in a factored form function:
f(x) = a (x + r)(x + s)

Answer 16

They are the roots of the quadratic. The two numbers added = b and the two number multiplied equal c in the standard form.

Question 17

17-12

how to know what the h and k stand for in the vertex form of the quadratic function. f9x) = a(x -h)² + k

Answer 17

The h is the x value and the k is the y value of the ordered pair located at the vertex of the graph.

Question 18

17-13, 17-14

write a function numerically

Answer 18

Create a table showing the x values in the first column and the F(x) or G(x) etc. values–the output values in the second column.