Even/Odd Functions
Even functions are symmetric about what line?
Y-Axis
What is the first step when solving an inverse equation?
Swap x and y
Solve for x:
25x+1 = 5x+3
x = 1
A line that is parallel to the line y = 3x + 8 would have a slope of what?
3
What is the domain of the function f(x) = x?
{-infinity, infinity}
What trigonometric function (sine, cosine, tangent) is even?
cosine
What is the inverse of y = 2x + 3?
y-1 = (x - 3)/2
What is the y-intercept of the function f(x) = 10(0.75)x?
(0, 10)
The equation 2x + y = 14 is written in standard form. Rewrite the equation in slope-intercept form.
y = -2x + 14
Simplify: (a3b)(a2b4)
a5b5 or (ab)5
Odd functions are symmetric about what?
The origin; (0, 0)
If you check by composition, f(f-1(x)) should always be equal to what?
x
Exponential functions will never cross what line unless shifted?
X-axis or y = 0
(This is called a horizontal asymptote.)
The point-slope form of the equation
y - 3 = 4(x + 1)
indicates that the line passes through what point?
(-1, 3)
Consider: (x + 7)/(x - 4)
For what value of x will the equation be undefined?
If we replace x with (-x) and the function stays exactly the same, is the function odd, even, or neither?
Even
What kind of function is the inverse function of any exponential function?
logarithmic function
Using the variables A, P, r, n, and t, what is the formula for compound interest?
A = P(1 + r/n)nt
In the piecewise function:
f(x) = { 2x + 7 when x<1
f(x) = { -0.5x + 4 when x >1
f(x) = {2 when x = 1
what is the value of f(x) when x = -4?
-1
If the expression 2x + 5 is equal to 13 for some value of x, what is the value of 4x + 9 for the same value of x?
2x + 5 = 13
x = 4
4(4) + 9
= 25
For the function f(x) = x(x2 + 1), is this an odd, even, or neither kind of function?
Odd; after distributing, x(x2 + 1) = x3 + x, which has all odd exponents
What is the inverse function of y = (2/3)x + 5?
y-1 = (3/2)(x - 5) or (3x - 15)/2 or 3(x - 5)/2
If the expression (1/x3)2 was written in the form xn, what would be the value of n?
n = -6
Rewrite the equation in slope-intercept form.
y - 5 = 2(x - 4)
y = 2x - 3
Write (x + 4)2 in standard form.
x2 + 8x + 16