Linear Functions
Is the following relation a function? Why or why not? (6, 0), (-3, 2), (2, 1), (-2, 1), (-3, 2)
No, because the input value (-3) is associated with two different output values (2 and 2).
Consider the following quadratic function in vertex form:
f(x) = 3(x − 2)2+ 2
What is the vertex?
(2, 2)
Divide 12x2 by 4x.
3x
f(x) = 500(1.07)x
What is the original amount?
500
Solve for x in the equation:
(x-1)/(2x+3) = 3/x
x = -3/5
Find the slope of the line through the points (6, 3) and (−4, 2).
1/10
f(x) = −3(x + 1)2 − 1
What is the axis of symmetry?
x=−1
Divide 16x3y2 by 8xy.
2x2y
f(x)=433(.56)x
What is the rate?
.56
Find the vertical asymptote(s) of the function f(x)=x2-4/x-2
x=2
What is the equation of a line parallel to y=1/2x+1 that passes through the point (2,−3)?
y = 1/2x - 4
What are the solutions to the quadratic equation
x2-5x+6=0?
x=2
x=3
Divide 10x4-5x2+15x by 5x.
2x3-x+3
What is the expected amount after 2 years? Round to the nearest hundreth.
495.77
Determine the domain of the function g(x)=1/x2-9
All real numbers except x=3 and x=-3
What is the equation of a line perpendicular to y=-3/4x+2 that passes through the point (5,1)?
y = 4/3x - 17/3
What are the solutions to the quadratic equation 2x2−5x+3=0?
x=1
x=3/2
Divide 4x3-7x2+3x+10 by 2x-1.
2x2-3x-7
log687 = x
Convert logarithm into exponential form.
6x=87
Find the horizontal asymptotes of the following rational function: f(x) =x3−2/x2−9x+4
None
Solve the system of linear equations by using either substitution or elimination:
2x+3y=10
x-y=4
x=6
y=2
Determine the vertex of the quadratic function given by f(x)=-4x2+16x-9.
(2, 7)
Divide 3x4+2x3-5x2-4x+8 by x2-2x+1
Solve the following exponential equation. Round to the nearest tenth.
10x+2 = 4000
x = 1.6
Find the slant asymptotes of the following rational functions: f(x) =x2−2x−7/x−4
y=x+2