Functions
Solve for f(2).
f(x)=2x+3
f(2)=2(2)+3
f(2)=4+3
f(2)=7
Determine if the sequence below is arithmetic, geometric, or neither.
110, 100, 90, 80, 70, 60...
Arithmetic
110, 100, 90, 80, 70, 60...
What is the common ratio (multiplier) for the following exponential function?
f(x)=2(3)x
Common Ratio (Multiplier) = 3
Solve for x.
x2=16
x=4 and x=-4
What is the maximum or minimum of a quadratic?
The vertex.
Solve for h(3).
h(x)=x2-5
h(3)=(3)2-5
h(3)=9-5
h(3)=4
Determine if the sequence below is arithmetic, geometric, or neither.
4,16, 64, 256, ...
Geometric
4,16, 64, 256, ...
Evaluate f(0).
f(x)=2(3)x
f(0)=2(3)0
f(0)=2(1)
f(0)=2
Solve for x using the Zero Product Property.
(x+2)(x-6)=0
(x+2)(x-6)=0
x+2=0 x-6=0
x=-2 and x=6
What is axis of symmetry?
y=3(x-2)2+4
Axis of Symmetry: x=2
Solve for g(-4).
g(x)=x-7
g(-4)=-4-7
g(-4)=-11
Determine if the sequence below is arithmetic, geometric, or neither.
0, 1, 4, 9, 16, 25, ...
Niether
0, 1, 4, 9, 16, 25, ...
What is the starting point for the following exponential function?
f(x)=25(1.05)x
Starting Point: (0, 25)
Factor out the GCF.
10x2+5x
5x(2x+1)
What is the y intercept?
y=x2-4x+5
Plug in x=0
y=(0)2-4(0)+5
y=5
Answer: (0,5)
Solve for q(-5).
q(x)=-x-6x
q(-5)=-(-5)-6(-5)
q(-5)=5-(-30)
q(-5)=35
Write the equation for the arithmetic sequence.
15, 20, 25, 30...
t(n)=5n+10
What is the common ratio (multiplier) for the following exponential function?
f(x)=3(1/3)x
Common Ratio: 1/3
Factor the quadratic.
x2+8x+12
(x+2)(x+6)
What is the vertex?
y=3(x-2)2-13
Vertex: (2, -13)
Solve for r(-3)
r(x)=-x2-6x-24
r(-3)=-(-3)2-6(-3)-24
r(-3)=-(9)-6(-3)-24
r(-3)=-9-(-18)-24
r(-3)=-9+18-24
r(-3)=9-24
r(-3)=-15
Write the equation for the geometric sequence.
400, 200, 100, 50,...
t(n)=800(1/2)n
If a population starts at 10,000 people and is decreasing by 3% each each. What would the population after 5 years?
Equation: y=10,000(1-0.03)x
y=10,000(0.97)x
Plug in x=5. y=10,000(0.97)5 and simplify.
After 5 years, the population will be around 8,587 people.
Solve this quadratic.
26=1+x2
26=1+x2
-1 -1
25=x2
+/-5 =x
x= 5 and x=-5
What is the vertex?
y=4(x+2)2+5
Vertex: (-2,5)