University of Idaho College Interval Notation in Algebra Functions Questions

Let f(x) = 5x + 5 and g(x) = 2×2 + 5x.
After simplifying,
(fog)(x) =
Complete the description of the piecewise function graphed below. Use interval notation to indicate
the intervals.
6
5
3
Od
.
-7
-6
-5
-4
-2
3
5
– 1
8
-2
-3
-4
-5
d
-6+
{ 2 if x E
f(x) =
=
{ 1
if X E
{ -1 if x E
Question Help: Video
Consider the equation: 22 – 10x + 21 = 0
A) First, use the “completing the square” process to write this equation in the form (x + D)2 = E
and enter your results below.
x2 – 10x + 21 = 0 is equivalent to:
=
Preview left side of eqn:
B) Solve your equation and enter your answers below as a list of numbers, separated with a comma
where necessary.
Answer(s):
Consider the function in the graph to the right.
The function has a maximum of
at x =
10+
19
The function has a minimum of
6
at x=
5
4
3
The function is increasing on the interval(s):
2
1
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1
4 5
6
7
8 9 10
The function is decreasing on the interval(s):
-2
-3
-4
-5
-6
The domain of the function is:
-7
-8
-9
-10
The range of the function is:
Let f(x) = x + 1 and g(x) = x – 1.
With the following stephs, determine whether f(x) 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?
=
Suppose that you are holding your toy submarine under the water. You release it and it begins to
ascend. The graph models the depth of the submarine as a function of time.
What is the domain and range of the function in the graph?
1
t (time)
4 5 6 7 8
1
ܢ ܝ ܝ ܛ ܥ ܪ
-7
d (depth)
-8+
a
D:
1
– 2
5
4
4
3
2
1
-5 -4 -3
1
2 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.
Express ✓–64 as a complex number (in terms of i):
✓-64
Consider the equation: x2
6x – 27 = 0
A) First, use the “completing the square” process to write this equation in the form (x + D)= E
and enter your results below.
x2 – 6x – 27
=
O is equivalent to:
(x +11)
Preview left side of eqn:
B) Solve your equation and enter your answers below as a list of numbers, separated with a comma
where necessary.
Answer(s):