Functions
Given that
f(x)=x/3+11
evaluate the following,
a. f(-12)
b. f(x) = -12
a. 7
b. -69
Factor completely
6x^2-5x-4
(2x+1)(3x-4)
Simplify
(12x^6)/(6x^6)
2x^6
Solve for m
z = k+a/m
m = a/(z-k)
A rocket is fired upwards following a path given by
y=-16x^2+112x
where y represents the height in feet above the ground and x represents time in seconds since the rocket was fired.
Determine how many seconds it takes for the rocket to reach ground level.
7 seconds
Use the function shown in the table to answer the following
x: 2 4 6 10
f(x): 10 20 30 50
a. f(10) =
b. f(x) = 10
a. 50
b. 2
Factor completely
8x^2-18y^2
2(2x+3y)(2x-3y)
3x^0
3
Solve for w
f=k/w
w=k/f
Graph the following inequality and name one possible solution.
y>4x+2
(-6,3)
(-2,2)
(-4,4)
(-5,2)
How can you determine if a graph is a function? if a table is a function?
Passes the vertical line test
No repeating y values
Factor completely
2x^3-4x^2+3x-6
(x-2)(2x^2+3)
Solve
2^(3x+7)=16
x = -1
Time (x): 2 4 8 14 20
Temp: 44.7 36.8 29.2 22.3 15.1
a. Find an exponential equation that best represents the data using exponential regression on your calculator. Round to the nearest hundredth.
b. Use your equation to predict the temperature of the water after 48 hours have elapsed.
c. Use the equation to estimate the time, x, in hours that the temperature of the water was at exactly 30 degrees.
a.
y = 47.97(.94)^x
b. 2.5
c. 7.6 hours
Solve algebraically
2x+3y=6
4x+2y=-4
(-3,4)
Write an equation using function notation that represents the following. You currently have $475 in a bank account that pays no interest. You earn $150 at work each week. Write a formula for the balance B, in dollars, in the account after t weeks.
B(t) = 475+150t
x^4-16
(x^2+4)(x+2)(x-2)
x^2*x^5
x^7
If $380 is invested in a savings account that earns 5% interest per year, determine the amount in the account at the end of 15 years? Round to the nearest dollar.
$790
Solve graphically
y = 7-3x
2y-4=-x
(2,1)
Given that f(x) = 2x-10 and g(x) = x+3 solve the following
a. f(x)+g(x)=32
b. f(x) = g(x)
a. x = 13
b. x = 13
10y^3-35y^2+30y
5y(y-2)(2y-3)
Solve
50(1.03)^(x/12)=230
x = 619.5
3(2x+2) = 6x+6
Infinite solutions
A football player attempts to kick a football over a goal post. The path of the football can be modeled by the function where d is the horizontal distance from the kick and h(d) is the height of the football above the ground, when both are measured in feet.
Determine the vertex of h(d). Interpret the meaning of this vertex in the context of the problem.
The goal post is 10 feet high and 24 feet away from the kick. Will the ball be high enough to pass over the goal post?
(19,14) When the ball has traveled a horizontal distance of 19 feet, the ball was at a height of 14 feet.
(24,10) Yes, the ball will be high enough because at distance 24 feet, the height of this player's ball was 13 feet (higher than 10 foot goal post)