Linear Functions
Find g(x), where g(x) is the translation 3 units down of f(x)=x.
g(x)=x-3
Find g(x), where g(x) is a translation 14 units up of f(x) = x2-6.
x2+8
The graph of f(x) = x^3 is reflected across the x axis. The graph is then translated 11 units up and 7 units left. Write the equation of the function.
g(x) = -(x+7)3 + 11
Simplify the radical expression √(x12).
x6
Tell whether the function represents exponential growth or exponential decay: y = (⅔)x.
Exponential decay
Find g(x), where g(x) is the translation 5 units right and 8 units up of(x)=x.
g(x)=(x-5)+8
If f(x)=1/16(x-3)2+3 has a focus at point (3, 7) what is the directrix?
y = -1
Determine whether the following function is even, odd, or neither: f(x) = -x3 + 2x - 9.
neither
Add. Write your answer in the simplest form.
-2√ 4 +10√ 2.
6√ 2
Find f(x) = ⅓(6x) when x = 2.
12
There is a line that includes the point (0, 0) and has a slope of 5. What is its equation in slope-intercept form?
y=5x
Write a rule in intercept form for the graph of a function f(x) that touches the point (0, 15) and touches the x-axis at points (5, 0) and (9, 0).
f(x) = 3(x-5)(x-9)
Factor x3 - 125 completely.
(x - 5)(x2 + 5x + 25)
Simplify the radical expression 5√ x20y13.
x4y2 5√ y3
State the growth or decay rate of y = a(0.5)t/12
6% decay
How does h(x)=x–1 change over an interval in x of length 3?
h(x) increases by 3
Solve 2x2 - 11 = -47.
3i√2, -3i√2
Factor z3 + 5z2 - 4z - 20 completely.
g(x) = 3(x-4)3 + 3
Simplify. Rationalize the denominator.
-10/(√6-√3)
(-10√3-10√6) /3
You take a 325 milligram dosage of ibuprofen. During each subsequent hour, the amount of medication in your bloodstream decreases by about 29% each hour. Write an exponential decay model giving the amount y (in milligrams) of ibuprofen in your bloodstream t hours after the initial dose.
y = 325(0.71)t
Find g(x), where g(x) is a reflection in the y-axis followed by a horizontal stretch by a factor of 3 and a translation 5 units right of f(x) = -3x.
g(x) = 9(x - 5)
Write y = x2-12x+18 in vertex form.
y = (x - 6)2 - 18
Determine whether the binomial is a factor of the polynomial: f(x) = 2x3 + 5x2 - 37x - 60; x - 4.
It is a factor.
Simplify the expression (16xy/xy)-7/4. Assume all variables are positive.
1/128
You deposit $5000 in an account that pays 2.25% annual interest. Find the balance after 5 years when the interest is compounded quarterly.
$5593.60