Grantham University Week 5 Evaluating Functions Work Sheet Paper

Evaluate the function ƒ(x) = 6x – 5 at ƒ(1)

Find all real values of x such that ƒ(x) = 0 for ƒ(x) = 42 – 6x

1
To evaluate a function, we:
Multiply f times the given number or expression
Substitute its variable with a given number or expression
Multiply the variable times the given number or expression
All of the answers are correct
To visually determine if a graph represents a function or not, we can use:
Vertical Line Test
Horizontal Line Test
Domain and Range Test
There is no way to determine from a graph.
The table below describes a function.
Input
Value
Output
Value
2001
2002
2003
2004
2005
30
60
30
50
40
True
False
Evaluate the function ƒ(x) = 6x – 5 at ƒ(1)
2
1
-1
0
2
What is the range of a function? Show your work
Find all real values of x such that ƒ(x) = 0 for ƒ(x) = 42 – 6x
7
5
9
6
8
What is the domain of the function?
The set of “x” values that will produce a “y” value
The set of “y” values that will produce an “x” value
All real numbers
Impossible to be determined
Find the zeroes of the function algebraically. Write the answer, if applicable, in fraction form. Show
your work
ƒ(x) = 2×2 – 3x -20
3
Find (ƒ+g)(x) for ƒ(x) = x+3, g(x) = x – 3
2x
3x
-2x
2x+6
Find (ƒ-g)(x) for ƒ(x) = x + 6, g(x) = x – 6
2x – 12
12
2x – 6
2x + 12
Find (ƒg)(x) for:
7×3 + 6×2
7×3 – 6×2
7×2 – 6×3
7×2 + 6×3
4
Find ƒ ∘ g for:
x2
(x – 5)2
(x + 5)2
x2 – 5
Select the correct description of right-hand and left-hand behavior of the graph of the
polynomial function.
Falls to the left, rises to the right.
Falls to the left, falls to the right.
Rises to the left, rises to the right.
Rises to the left, falls to the right.
Falls to the left.
Describe the right-hand and the left-hand behavior of the graph of
Because the degree is odd and the leading coefficient is positive, the graph falls to the
left and rises to the right.
Because the degree is odd and the leading coefficient is positive, the graph rises to the
left and rises to the right.
Because the degree is odd and the leading coefficient is positive, the graph falls to the
left and falls to the right.
Because the degree is odd and the leading coefficient is positive, the graph rises to the
left and falls to the right.
5
Using an online calculator, sketch the graph of the function to find the zeroes of the
polynomial.
0,2,3
0,2,-3
0,-2,3
1,2,3
Any non-zero number divided by zero is: Show your work
Select the graph of the function and determine the zeros of the polynomial: f(x) = x2(x-6).
Indicate which graph below is the correct one: 1st, 2nd, 3rd, or 4th.
6
7
The height, h(x), of a punted rugby ball is given by
where x
is the horizontal distance in feet from the point where the ball is punted. How
far, horizontally, is the ball from the kicker when it is at its highest point? (Hint:Examine
the vertex of this quadratic function)
28 feet
13 feet
18 feet
23 feet
The profit P (in hundreds of dollars) that a company makes depends on the amount x (in
hundreds of dollars) the company spends on advertising according to the model. P(x) = 230
+ 40x – 0.5×2 What expenditure for advertising will yield a maximum profit? (Hint:
Examine the vertex of this quadratic function)
40
0.5
230
20
The total revenue R earned per day (in dollars) from a pet-sitting service is given by R(p) =
-10p2 + 130p where p is the price charged per pet (in dollars). Find the price that will yield a
maximum revenue.
$7.5
$6.5
$8.5
$10.5