University of Idaho College Algebra Functions Practice Questions

Given the following functions, evaluate each of the following:f(x) = x2 – 4
g(x) = x + 2
(f + g)(2) =
(f – g)(-2) =
(fºg)( – 4) =
()
(-3)
=
Function Operations
Given the functions:
f(2) = 2x
g(x) = 2x
3
h(x) = 10.2
17x + 3
Determine each of the following.
Give your answers as simplified expressions written in descending order.
g(x) + h(x) =
Find and simplify g(x) + (x)
h(x) – g()
=
Find and simplify h(x) – g(2)
f(x).h(x) =
Find and simplify f(x)h()
h(2)
9(2)
=
h(2)
Find and simplify hint: you will need to
g(x)’
factor h(x)
g(2)
The domain restriction for is
f(a)
X +
Use the graphs to evaluate the expressions below.
6
f(x)
8(x)
5
4
3
WW
2
1
х
2
3
4
6-1
1
2
-1
+-
f(g(3)) =
=
g(f(5)) =
f(f(2)) =
g(g(4))
=
Let f(x) 2x + 2 and g(x) = 3×2 + 2x.
After simplifying
(fog)(x) =
g) =
Let f(2)
=
1
and g(2)
X – 7
2
+ 7.
х
Find the following functions. Simplify your answers.
f(g(x)) =
g($(2))
=
Move the slider k so that the graph of y = x2 gets shifted up 2 units. Then type the new function,
f(x) in the answer box
6
5
4
3
2
1
-4
-3
-2
-1
1
2
3
4
-1
f(x) = 22
k= 0.00
-2
–
o
+ 1
Don’t forget to shift the graph up.
Using function notation, i.e. f(x) = , enter the function that results from the transformation.
=
Move the sliders h and k so that the graph of y xgets shifted up 3 units and to the right 1 units.
Then type the new function, f(a) in the answer box
4
3
2
1
-4
-3
-2
-1
o
1
2
3
4
f(x) = x2
-1
h = 0.00
-2
k= 0.00
– 0 ++ î →
Don’t forget to shift the graph.
Using function notation, i.e. f(x) = , enter the function that results from the transformation.
If the formula y = xo is changed by adding three as shown in red below.
f(x) = (x + 3) 3
Which values would be most directly affected by the change?
Select an answer
What effect would it have on the graph?
Select an answer
If the formula y = x3 is changed by adding three as shown in red below.
f(x) = (x + 3)3
Which values would be most directly affected by the change?
✓ Select an answer
It would directly affect the x-values.
It would directly affect the y-values. he graph?
It would have no effect.
Select an answer
If the formula y = x3 is changed by adding three as shown in red below.
f(x) =
=
(x + 3)3
Which values would be most directly affected by the change?
Select an answer
What effect would it have on the graph?
Select an answer
D
It would have no effect.
It would shift all the points to the left three.
It would shift all the points down three.
It would shift all the points up three.
It would scale all the points by a factor of three.
It would shift all the points to the right three.
5
4
3
2
1
1
2
3
4
5
-5 -4 -3 -2 -1
-1
-2
-3
-4
-5+
다.
Write an expression for the function graphed above:
Enter abs(x) for |2C.
6
5
4
3
2
1
-6 -5 -4 -3 -2 -1
-1
-2
-3
-4
-5
-6
a
The graph above is a transformation of the function x2.
Give the function in the graph above.
g(x)
=
Assume that the function f is a one-to-one function.
(a) If f(5) = 4, find f -1(4).
Your answer is
=
4, find f( – 4).
(b) If f-1( – 4)
Your answer is
Let f(x) = 8x + 10
f-‘(x) =
Let f(x) = (x – 3)2
Find a domain on which f is one-to-one and non-decreasing.
Find the inverse of f restricted to this domain.
f-1(x) =
Let f(x) = x + 2 and g(2) = x – 2.
=
With the following stephs, determine whether f(a) and g(x) are inverses of each other:
(a) f(g(x)) =
(b) g(f(x)) =
(c) Are f(x) and g(x) inverses of each other?
Given the following functions, evaluate each of the following:
f(x) = x2 – 4x
5
g(2)
= X
– 5
(f + g)(5) =
=
(f – g)(2) =
=
(f.g)( – 2) =
=
()
(-3)
=
The admission fee at an amusement park is $3.75 for children and $5.20 for adults. On a certain
day, 286 people entered the park, and the admission fees collected totaled $1232. How many
children and how many adults were admitted?
number of children equals
number of adults equals
A movie theater has a seating capacity of 181. The theater charges $5.00 for children, $7.00 for
students, and $12.00 of adults. There are half as many adults as there are children. If the total ticket
sales was $ 1296, How many children, students, and adults attended?
children attended.
students attended.
adults attended.
Write the system of equations as an augmented matrix.
2d +
5c
34
— 66 +
– 76
2d +
40
– 51
– 2b +
6d
2c
40
Find the determinant of matrix A
(-30
-4 -5
– 3 0
det(A)
The plot below represents the function f(x):
8+
7
6
5
4
3
2
1
-5 -4 -3 -2 -1
-1
1 2 2 3 4 5
-2+
Evaluate f(4):
f(4) =
=
Solve f(x) = 4:
X =
Suppose f(a)
=
– x2 + 10x – 9. Compute the following:
A.) f( – 3) + f(2)=
B.) f(-3) – f(2) =
6
5
4
3
2
1
-6 -5
1 2
3 4
-3 -2 -1
– 1
-2
a
-3
-4
-5
-6+
Write the domain of the function using interval notation.
Given the function:
8x – 8
f(x) =
8x – 16 x > 0
S 8x
x < 0 { = Calculate the following values: f( - 1) = f(0) = f(2) = Sketch a graph of f(x) = = 3 if x < - 1 - 2x + 1 if –1 < x < 2 1 if X > 2
5
4
3
2
1
-5
1
2
3
-4 -3 -2 -1
– 1
-2
-3
-4
-5
Clear All Draw:
Note: Be sure to include closed or open dots, but only at breaks in the graph.
Consider the function graphed at right.
5
4
The function has a
Select an answer
of
at x =
3
2
1
The function is increasing on the interval(s):
-4
1
2 3
4 5
-2 -1
– 1
-2
The function is decreasing on the interval(s):
-3
-4
5
d
Sketch a graph of f(x)
–
-1 if x < - 1 2x + 1 if –1 < x < 2 4 if X > 2
5
4
3
2
1
-5 -4 -3 -2 -1
1
2
3 4
– 1
-2
-3
-4
-5
Clear All Draw:
Solve the equation: 22 – 52 + 25 = 0. Fully simplify all answers, including non-real solutions.
z =
Consider the parabola given by the equation: f(x) = 2×2 – 12x + 2
Find the following for this parabola:
A) The vertex:
B) The vertical intercept is the point
C) Find the coordinates of the two x -intercepts of the parabola and write them as a list, separated
by commas:
It is OK to round your value(s) to to two decimal places.
You are working with a quadratic equation and constructing the following graph.
5+
4
-8
2
2
4
5 6
7
8
-4
1-5+
to
Identify the vertex of the parabola:
Remember that the vertex is a point!
Identify the y-intercept of the parabola:
Remember that the y-intercept is a point!
Identify the x-intercepts: and
Remember that the x-intercepts represent points on the graph!
Given the x-intercepts above, write an equation for the parabola in factored form:
.y =
Hint: Think about the zero-product property.
=
Write an equation for the axis of symmetry:
Put the equation y = x2 + 22x + 117 into the form y = (x – h)? + k:
Answer: y =
Find the degree of the term – 40°:
Find the degree of the term – 2:
Find the degree of the term 3×6:
Find the degree of the term 6×5:
Find the degree of the polynomial – 4×3 – 2 + 3×6 + 6×5:
Ouestion Heln.
Video
Describe the end behavior (long run behavior) of f(x)
=
24
As 2 →
~, f(a)
->
?
As x + 00, f(x)
T
?
Given the function f(x) = (x – 6)(x + 4)(x – 5)
its y-intercept is
its x-intercepts are
The polynomial of degree 5, P(x), has leading coefficient 1, has roots of multiplicity 2 at x = = 3 and
– 0, and a root of multiplicity 1 at x =
– 3.
X =
Find a possible formula for P(x).
P(x)
=
5 and a root of multiplicity 1 at
The polynomial of degree 3, P(x), has a root of multiplicity 2 at x
– 1. The y-intercept is y = – 17.5.
X =
Find a formula for P(a).
P(x) =
Write an expression in factored form for the polynomial of least possible degree graphed below.
5+
4
3
2
1
-5
4
-3
2
-2 -1
-1
4
5
-2
-3
-5+
Q
y(x) =
You are working with a quadratic equation and constructing the following graph.
5+
4
3
-8 -7 -6 -5
-4-13-2
6
7 8
-3
-4
-5+
Identify the vertex of the parabola:
Remember that the vertex is a point!
Identify the y-intercept of the parabola:
Remember that the y-intercept is a point!
Identify the x-intercepts: and
Remember that the x-intercepts represent points on the graph!
Given the x-intercepts above, write an equation for the parabola in factored form:
.y:
Hint: Think about the zero-product property.
Write an equation for the axis of symmetry:
Given the function f(x) = (x – 1)(x + 2)(x – 5)
its y-intercept is
its x-intercepts are
Ouestion oln.
Video
You are working with a quadratic equation and constructing the following graph.
5+
4
3
2
-8 -7 -6 -5 -4
6
8
-3
-4
-5+
to
Identify the vertex of the parabola:
Remember that the vertex is a point!
Identify the y-intercept of the parabola:
Remember that the y-intercept is a point!
Identify the x-intercepts: and
Remember that the x-intercepts represent points on the graph!
Given the x-intercepts above, write an equation for the parabola in factored form:
.y =
Hint: Think about the zero-product property.
Write an equation for the axis of symmetry:
Given the function f(x) = (x – 1)(x + 2)(x – 5)
its y-intercept is
its x-intercepts are