Relations and Functions
Is the set of of ordered pairs a function? Why?
{(2,3), (2,5), (4,1)}
No, because the input 2 has more than one output (3 and 5)
Write 5,600 in scientific notation.
5.6*10^3
Simplify:
(x+5)+(3x-2)
4x+3
Simplify:
x^3*x^2
x5
Plotting the point (3, -2): which quadrant is it in?
Quadrant IV (4)
What is the domain of the relation?
{{-1,4), (0,2), (3,-1)}
{-1, 0, 3}
Convert from scientific notation to standard notation.
3.9*10^-4
0.00039
Subtract:
(6x^2-4x+1)-(2x^2+x-3)
4x^2-5x+4
Simplify:
x^7/x^3
x4
What is the slope of a horizontal line?
m = 0
Determine if the equation represents a function.
y=3x^2-7
Yes, each x gives exactly one y.
Multiply:
(2*10^5)(3*10^2)
6*10^7
Multiply:
(x+2)(x-7)
x^2-5x-14
Evaluate: 2-3
1/8
Find the slope between the points (1, 4) and (3, 10).
m = 3
Find
f(8)=2x-5
What is 11?
Divide:
(7.2*10^6)/(9*10^2)
8*10^3
Multiply:
(3x-3)(3x^2+x+4)
6x^3-x^2-x-12
Simplify: (3x2)3
27x6
Write the equation of a line with slope 2 passing through (-1, 5).
y=2x+7
A gym charges $25 sign-up fee plus $15 per month. Write a function C(m) to represent the total cost after m months, and find the total after 6 months.
C(m)=15m+25; $115
A cell divides every 6 hours. A scientist begins with 3.5 * 103 cells. After one day (24 hours), the population quadruples. Express the new population in scientific notation.
1.4*10^4
A rectangular garden has a length of (2x + 5) meters and a width of (x - 3) meters. Write an expression for the area and simplify.
A=(2x+5)(x-3); 2x^2-x-15
The intensity of light from a bulb decreases according to the function below where d is the distance in meters. Find the intensity at 5 meters.
I(d)=100/d^2
I(d)=100/5^2=100/25=4
A rideshare company charges $1.50 per mile plus a flat fee. A 6-mile trip costs $16. Determine the flat fee and write the linear equation for total cost C(m).
C(m)=1.5m+7