Linear Functions
What is the standard form of a linear equation?
y = mx + b
(2-3i)(3+6i)
24 + 3i
Find the x and y intercepts:
f(x) = (x+2)/(x-5)
y = -2/5
x = -2
Rewrite ln(s) = t as an exponent.
et = s
What is the range of the sin funtion?
-1 <y< 1
What is the slope of this linear equation?
3x + 6y = 14
m = - 1/2
Find the vertex of the quadratic function:
x2 - 4x -5
2
Find the vertical asymptotes:
f(x) = (x2 + 1)/(x2 - 4)
x = 2
x = -2
State the domain, range and y-intercept of:
f(x) = 3.5 (2)x
D: All real numbers.
R: y>0
Y intercept: (0,3.5)
A 15 foot ladder leans against the wall so that the angle with the ground is 70 degrees. How high does the ladder reach up the wall?
14 feet
Are these lines parallel, perpendicular or neither?
2x - 6y = 12
-x + 3y =1
Parallel
Determine the end behavior:
2x2(1+ 3x - x2)
Down - Up
Find the inverse function:
f(x) = 2x3 - 3
f-1(x) = (x/2 + 3/2)1/3
State the domain and vertical asymptote of:
f(x) = ln(4x + 20) - 17
D: x > -5
Vertical Asymptote: x = -5
What is the amplitude and midline of :
f(x) = -3cos(x) + 3
A: 3
M:3
Write the equation for the line perpendicular to
f(x) = 5x - 1 and passing through the point (5,20)
y = -1/5 x + 21
Find the degree and the leading coefficient:
3x2(3 - 6x - 2x2)
Degree: 4
Leading Coefficient: - 6
Find the slant asymptote:
f(x) = (x2 - 1)/(x+2)
y = x - 2
Condense the expression to a single logrhythm:
3log(v)v + 6log(w) - 3log(u)
log (v3w6/u3)
What is the phase shift and period of:
f(x) = 4csc(5x + 10)
PS: 10 to the left.
Period is 2(pi)/5
Find the point of intersection for the two linear functions:
x=y+6
2x - y = 13
(7,1)
Find all the zeros:
x5 + 4x4 + 4x3
0,0,0,-2,-2
Use long division to find the quotient and the remainder:
(3x4 - 4x2 + 4x + 8)/(x + 1)
3x3 - 3x2 - x + 5 remainder = 3
Find the exact solution for:
9 + 6ln(x + 3) = 33
x = e4 - 3
Find the length of the other two sides of the right triangle.
cos(B) = 3/5 and a = 6
b=8
c = 10