Recall two different function notations: f(x) = x – 2 or f:x x – 2 (This 2nd

notation is seldom used)

D Relation - Any set of ordered pairs

OR any equation that creates relationships between two variables.

D Function – Any set of ordered pairs in which no x-coordinate is used twice (y's can be repeated, but not x's)

OR any equation that creates a correspondence between two variables, but no x is repeated.

Hint: Vertical Line Test. If any vertical line would pass through a graph twice that would show that two points have repeated the same x coordinate and thus, that relation is NOT a function.

1. Write YES or NO to tell whether the relation on each graph represents a function.

A.___________ B. ___________ C. ___________ D. ___________ E. ________ F. _______

YES NO 2. Is the (discrete) relation {(3, 1), (-3, 1), (0, 1)} a function?

YES NO 3. Is the (discrete) relation {(5, 1), (-5, 2), (5, 3)} a function?

YES NO 4. Is the (continuous) relation y = – ½ x – 5 a function? (Does its graph pass the vertical line test?)

YES NO 5. Is x = 5 a function? (Does its graph pass the vertical line test?)

YES NO 6. Is y = 5 a function? (Does its graph pass the vertical line test?)

D Domain – the set of all x-coordinates in a relation or function D Range – the set of all y-coordinates in a relation or function

________________________7. What is the domain of the function {(-9, 2), (7, 0), (3, 2)}?

________________________8. What is the range of the function{(-9, 2), (7, 0), (3, 2)}?

YES NO 9. Is the graph at the right a function?

________________________10. What is the domain of the graph at the right?

________________________11. What is the range of the graph at the right?

________________________12. What is the domain and range of f(x) = 5?

________________________13. What is the domain and range of f(x) = -2x + 5? Over

Algebra 2 w/ Trig

Semester Exam

Review 10 Functions

NAME ___________________________

Date :

(0, 6)

(– 6, 0) (6, 0)

Problems 9-11

Continuous relation

Discrete relation (discontinuous pts)

YES NO 14. Is the discrete relation at the right a function? ________________________15. What is the domain of the graph at the right? ________________________16. What is the range of the graph at the right? ________________________17. Which relation is continuous? (Prob 9 or Prob 14?) ________________________18. Which relation is discrete? (Prob 9 or Prob 14?) D Composite Function – evaluating one function inside another function. In #19-20, you will evaluate "p composite q" when you find p(q(x)). Note the alternate Composite notation: p q

______;_______;_________ 19. Given 1

p(x) x 34

and q(x) = 2x – 1. Find p(-8), q(7) and p(q(3)).

________________________20. Given p(x) & q(x) above, find the rule of p(q(x)).

________________________21. Given that f(-2) = 8 and f(3) = -2, list two ordered pairs on the graph of function f.

____________________________________22. Find the rule of linear function, f, if f(-2) = 8 and f(3) = -2.

Hint: What two points are given? Find slope. Use Pt-Slope Formula. Replace "y" with " f(x)" notation. Implied Domains: Unless a restricted domain is specified with a function, we assume the domain should include all real numbers that work in the rule of the function. Throw out any x values that would create a problem such as

a negative value under a square root (or a 4th, 6th or any root with an even index)

division by zero error

Examples: x 2

f (x) D{x : x 5}x 5

____________________________________23. Give the domain of b(x) x 2

____________________________________24. Give the domain of 2

x 1d(x)

x 9

____________________________________25. Give the domain of 3h(x) x 1

26. Twelve days after Joe began a diet he weighed 180 lb. After 16 days he weighed 177 lb. *Assume the

relation is a linear function. *Do you think a diet would continue progressing as a linear function for a long period of time?

____________________________________a. Find the rule (equation) of W(d) giving Alan's weight on day, d. ____________________________________b. How much did he weigh at the beginning of the diet? ____________________________________c. At this rate, when will he weigh 165 lbs?

g(x) 5 x D{x : x 5}

because5 x must benon negative

5 x 0 5 x

(0, 3)

Problems 14-16

(1, 1) (3, 1)

(3, 3) (4, 4)

(6, 5)

Recall two different function notations: f(x) = x – 2 or f:x x – 2 (This 2nd

notation is seldom used)

D Relation - Any set of ordered pairs

OR any equation that creates relationships between two variables.

D Function – Any set of ordered pairs in which no x-coordinate is used twice (y's can be repeated, but not x's)

OR any equation that creates a correspondence between two variables, but no x is repeated.

Hint: Vertical Line Test. If any vertical line would pass through a graph twice that would show that two points have repeated the same x coordinate and thus, that relation is NOT a function.

1. Write YES or NO to tell whether the relation on each graph represents a function.

A.___________ B. ___________ C. ___________ D. ___________ E. ________ F. _______

YES NO 2. Is the (discrete) relation {(3, 1), (-3, 1), (0, 1)} a function?

YES NO 3. Is the (discrete) relation {(5, 1), (-5, 2), (5, 3)} a function?

YES NO 4. Is the (continuous) relation y = – ½ x – 5 a function? (Does its graph pass the vertical line test?)

YES NO 5. Is x = 5 a function? (Does its graph pass the vertical line test?)

YES NO 6. Is y = 5 a function? (Does its graph pass the vertical line test?)

D Domain – the set of all x-coordinates in a relation or function D Range – the set of all y-coordinates in a relation or function

________________________7. What is the domain of the function {(-9, 2), (7, 0), (3, 2)}?

________________________8. What is the range of the function{(-9, 2), (7, 0), (3, 2)}?

YES NO 9. Is the graph at the right a function?

________________________10. What is the domain of the graph at the right?

________________________11. What is the range of the graph at the right?

________________________12. What is the domain and range of f(x) = 5?

________________________13. What is the domain and range of f(x) = -2x + 5? Over

Algebra 2 w/ Trig

Semester Exam

Review 10 Functions

SOLUTION KEY

Date :

(0, 6)

(– 6, 0) (6, 0)

Problems 9-11

Continuous relation

Discrete relation (discontinuous pts)

YES NO 14. Is the discrete relation at the right a function? ________________________15. What is the domain of the graph at the right? ________________________16. What is the range of the graph at the right? ________________________17. Which relation is continuous? (Prob 9 or Prob 14?) ________________________18. Which relation is discrete? (Prob 9 or Prob 14?) D Composite Function – evaluating one function inside another function. In #19-20, you will evaluate "p composite q" when you find p(q(x)). Note the alternate Composite notation: p q

______;_______;_________ 19. Given 1

p(x) x 34

and q(x) = 2x – 1. Find p(-8), q(7) and p(q(3)).

________________________20. Given p(x) & q(x) above, find the rule of p(q(x)).

________________________21. Given that f(-2) = 8 and f(3) = -2, list two ordered pairs on the graph of function f.

____________________________________22. Find the rule of linear function, f, if f(-2) = 8 and f(3) = -2.

Hint: What two points are given? Find slope. Use Pt-Slope Formula. Replace "y" with " f(x)" notation. Implied Domains: Unless a restricted domain is specified with a function, we assume the domain should include all real numbers that work in the rule of the function. Throw out any x values that would create a problem such as

a negative value under a square root (or a 4th, 6th or any root with an even index)

division by zero error

Examples: x 2

f (x) D{x : x 5}x 5

____________________________________23. Give the domain of b(x) x 2

____________________________________24. Give the domain of 2

x 1d(x)

x 9

____________________________________25. Give the domain of 3h(x) x 1

26. Twelve days after Joe began a diet he weighed 180 lb. After 16 days he weighed 177 lb. *Assume the

relation is a linear function. *Do you think a diet would continue progressing as a linear function for a long period of time?

_____________________________________________________ a. Find the rule (equation) of W(d) giving Alan's weight on day, d. _____________________________________________________ b. How much did he weigh at the beginning of the diet? _____________________________________________________ c. At this rate, when will he weigh 165 lbs?

g(x) 5 x D{x : x 5}

because5 x must benon negative

5 x 0 5 x

(0, 3)

Problems 14-16

(1, 1) (3, 1)

(3, 3) (4, 4)

(6, 5)