Evaluating Functions
If f(x) = -4x2-6x+9, evaluate f(-2).
-4(-22)-6(-2)+9
-16+12+9
5
What is the name of the test used to evaluate if a graph is a function?
Vertical line test
Fill in the blank: A polynomial is an expression with more than two _____________.
Terms
What is the domain of a function?
The set of input or x-values for which the function is defined.
What does the E stand for in GEMDAS?
Exponents
Fill in the letters below so that this set of data represents a function.
(4, 29) (a, 13) (17, 5) (20, d) (20, 7)
a= any number besides 4, 17, and 20
d=7
The function
The candy company sold 10 bags of candy and made $125 profit.
Write a binomial expression of the second degree with a leading coeffecient of 4 and a constant of -7.
4x2 -7
How can you determine the range of a function, given its domain?
Substitute the domain values into the equation and evaluate.
Give an example of a discrete variable.
Answers may vary.
Number of phones in a school, number of dogs at a dog park, number of tickets purchased to a concert.
f(x) = 4x-10
g(x) = x2- 7x +9
Find f(x)-2g(x)
(4x-10)-2(x2- 7x +9)
-2x2+18x -28
Draw the graph of a relation that is NOT a function.
Answers will vary, but they will all fail the vertical line test.
Simplify the following expression: 3(-3g-5) - 2 -2g
-11g - 17
*If you got -11g+1 then you forgot to distribute the negative into the second set of parentheses.
Ms. Jones and Ms. Riley create a function which uses the number of hours a student sleeps on average to predict his/her ACT scores.
Is the range of this function discrete or continuous? Explain how you know.
Discrete because you cannot get half points on the ACT.
What do we call a value that does not change?
Constant
Does the point (3, 9) lie on the graph of the function f(x) = x2-2x+13? How do you know?
No, because when you substitute 3 for x, you get 16, not 9.
The graph of the function displays how much money Regina has made based on how many cars she has washed in one day. How would you limit the output of this function?
Positive whole numbers only. Numbers of 30 are not realistic.
Write a polynomial that is twice the sum of x2+9 and 3x-15
2[(x2+9) + (3x-15)]
2x2 + 6x - 12
A function uses hours past 6 am to determine the number of people on a city bus. Determine an appropriate range for the output of this function.
Answers will vary. 0-50. No negative or half numbers.
Translate this into an algebraic expression: twice the sum of x-squared and four hundred fifty nine.
2(x2+459)
Write a function to describe your profit, f(x), when you open your own chick-fil-a franchise. You make $5,000 per day and x represents the number of days you have been open. Don't forget to include the $150,000 you invested in order to purchase the franchise.
Double points: Calculate your profit 12 days after opening.
f(x)= 5,000x -150,000
Double points: You're still DOWN $90,000
Is y2= x + 1 a function? Explain how you know.
No, you can have multiple outputs for the same input. For example, when x = 8, y= 3 AND -3
Let x%y be defined as x2+y2 - xy.
Find 3%-1
32+(-1)2 - (-1)(3)
9+1+3
13
A salon found that the amount of minutes it takes to cut someone's hair,
Range: 0 to 66
What is the property that says you can add or multiply numbers in any order?
Commutative Property