Basic Inequalities
Rewrite x<=4 in interval notation.
(-inf,4]
Rewrite |x-5|>=3 in interval notation.
(-inf,2] U [8,inf)
What is the formula for difference quotient?
f(x+h)-f(x)/h
What do m and b represent in y=mx+b?
m = slope
b= = y-intercept
f(x)=2x+2 if x<-1 and f(x)=-x-1 if x>=-1, is this function discrete or continuous?
Continuous
Rewrite 8< -5x+3 in interval notation.
(-inf,-1)
Rewrite |2x+4|<=10 in interval notation.
What is the difference quotient for f(x)=3x?
3
What is f(x+3) if f(x)=8x+4?
8x+28
If f(x)=2x+2 if x<-1 and f(x)=-x-1 if x>=-1, what is the domain and range of the function (in interval notation)?
Domain: (-inf,inf)
Range: (-inf,0]
Rewrite 13x+24<16-3x in interval notation
(-inf,-1/2)
Solve |x-2|=2x.
2/3
What is the difference quotient of f(x)=x?
1
Write the domain and range of the equation y=-x in interval notation.
Domain = (-inf,inf)
Range = (-inf,inf)
If f(x)=2x+2 if x<-1 and f(x)=-x-1 if x>=-1, where is the function increasing and decreasing (in interval notation)?
Increasing: (-inf,0)
Decreasing: (0,inf)
Rewrite -4<6x-10<=14 in interval notation.
(1,4]
Solve the equation: |8x+1|=3x.
No solutions
Find the difference quotient of f(x)=5x^2-4.
10x+5h
Find the value of k so that the line through the given points has the given slope. (2,-3) and (k, 7); m=-2
k=-3
If f(x)=|x| if x=<2 and f(x)=4x-6 if x>2, where is the function increasing and decreasing (in interval notation)?
Increasing: (0,inf)
Decreasing: (-inf,0)
Rewrite 2x-3< -4 or 3x+1>=4 in interval notation.
(-inf,-1/2) U (1,inf)
How is the function f(x)=|x| different than f(x)=-1/2|x-4|+3/4?
2. Wider
3. To the right 4
4. Up 3/4
Find the difference quotient of f(x)=3x^2+x.
6x+3h+1
What is the slope of a line that is perpendicular to a different line containing the points (-5,1) and (3,1)?
Undefined
If f(x)=|x| if x=<-2 and f(x)=4x-6 if x>2, what is the domain and range of the function (in interval notation)?
Range: [-2,inf)