Linear Functions
Determine the y-intercept and slope of f:
f(x)=(8/9)(x)-4
y-intercept: -4
Slope: 8/9
Use the square root property: (5x-2)2+9=0
x=(2+3i)/5, (2-3i)/5
f(2)=7
Solve for |x-5|=7
x=12 and x=-2
Solve and express your answer using interval notation:
-3x+4>2x-6
(-infinity,2)
Find the average rate of change of f on the interval [0,3] where f(x)=-2x+15.
-2
Use factoring: x2+7x+10=0
x=-2,-5
Does f(x)=-3x2+12x-5 have a maximum or minimum and what is it?
Solve for 5-|x-2|=2
x=5 and x=-1
Solve and express your answer using interval notation:
-2-3x (less than or equal to) 4-x < 10-2x
[-3,6)
If f is a linear function where f(-2)=1 and f(4)=13, find the formula for f(x).
m=2, y-intercept=5
f(x)=2x+5
Use completing the square: 3x2-18x+6=0
x=3+sqrt(7), 3-sqrt(7)
Sketch the graph of f(x)=-3x2+12x-5.
I'll determine if correct.
Solve for 3|(x-4)/3|=5
x=9 and x=-1
Solve and express your answer using interval notation:
-3x+2 (greater than or equal to) 11
or 4x-5 (less than or equal to) -17
(-infinity,-3]
Find an equation of the line perpendicular to the graph of f(x)=2x+5 and passing through the point (4,-1).
m=-1/2, y-(-1)=(1/2)(x-4)
y=(-1/2)x+1
Use the quadratic formula: 3x2-4x+5=0
x=(2+i sqrt(11))/3, (2-i sqrt(11))/3
A tennis player hits a high lob from an initial height of 4 feet above the court. The ball goes straight up into the air, and its height (in feet) after t seconds is given by
h(t)=-16t2+64t+4.
What is the height after 1 second?
52 feet
Solve for |x-2|+5=9
x=6 and x=-2
Solve and express your answer using interval notation:
|2x-7| (greater than or equal to) 7
(-infinity, 3] U [4, infinity)
A delivery company purchases a new delivery van for $12,000. The company estimates that after 5 years, the van will have a value of $2,000. Assume the value of the van depreciates linearly.
What is the value of the van after 3 years?
V(t)=12,000-2,000t
V(3)=12,000-2,000(3)= $6,000
Use any method: 2x2+5x=1
x=(-5+sqrt(33))/4, (-5-sqrt(33))/4
A tennis player hits a high lob from an initial height of 4 feet above the court. The ball goes straight up into the air, and its height (in feet) after t seconds is given by
h(t)=-16t2+64t+4.
How long does it take for the ball to reach its maximum height?
2 seconds
Solve for |3x+5|=|2-4x|
x=-3/7 and x=7
Solve and express your answer using interval notation:
|2x-3|>11
(-infinity,-4) U (7, infinity)