# Name ___________________________________ Introduction to Functions Date ___________________

```Name ___________________________________
Introduction to Functions
Date ___________________
Day 3 HW
(1) Graph f(x) = x + 3 and g(x) = |x| + 3 on the coordinate grid below. Explain how the functions
are the same and how they are different. Be specific and show all work!
y
10
8
6
4
2
x
-10
-8
2
-2
-4
-6
4
8
6
10
-2
-4
-6
-8
-10
(2) y = -2 x + 3 - 2  Describe the transformation(s) from y = |x|.
10
y
Domain
8
Range
6
4
Increasing
2
x
-10
-8
-6
-4
-2
2
4
6
8
10
-2
Decreasing
Positive
-4
Negative
-6
-8
End Behaviors
-10
(3) g(x) =
1
3
x
10
(4) When graphed on the same set of axes, in
how many points do the graphs of
y = |x| – 1 and y = –2 intersect?
y
8
6
4
2
x
-10
-8
-6
-4
-2
2
4
6
8
(1) 1
(3) 0
(2) 2
(4) 4
10
-2
-4
-6
-8
-10
Math 9R
(5) The graph at the right is a transformation of the absolute value function, f(x) = |x|.
a. Which of the following equations represents this graph?
(1) f(x) = |x – 3| – 4
(3) f(x) = | x + 4 | – 3
(2) f(x) = | x + 3 | – 4
(4) f(x) = | x – 4 | – 3
b. For what interval is the f(x) > 0?
c. What is the absolute minimum of this function?
d. What is the value of f(-1) – 3f(4)?
e. For what value(s) of x is f(x) = -2?
 For #6 – 11, write an equation for the given graphs or for the given description. Show work leading
(6)
(7)
(8) Write an equation for y = x left 3 units.
____________________
(9) Write an equation for y = − x up 6 units.
____________________
(10) Write an equation for y = - x down 5 units, right 3 units.
____________________
(11) Given the graph of f(x) = |x – 2| + 3, what would be the equation, g(x), for the same graph if it
was translated left one unit and down two units?
____________________
Math 9R
REVIEW
 Identify the domain and range of each relation, and determine whether the relation is a function.
(12) {(3, 6), (4, 7), (5, 8), (6, 9)}
(13) {(-1, 0.4), (1, 3), (-2, 1), (-1, 6)}
REVIEW (CONT.)
(14) Find the range of h(x) = -3x2 + 4 if the domain is {-2, 10, -1}.
(15) For which of the following functions is g(-2) > g(2)?
6
(1) g(x) = 6x2
(3) g(x) =
(2) g(x) = 6
(4) g(x) = 6 – x3
x
(16) On the following set of axis, create the graph of a function b(x) with the following
characteristics:
• Domain: x ≥ -4
• Range: 0 ≤ x < 3
• b(x) > 0: x > -4
• End Behaviors: right
• Is this function linear? Explain.
• Is this function increasing, decreasing, or both?
Math 9R
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