Show:
Simplifying Radicals
Properties of Hyperbolas
Simplifying Expressions with Same Bases
Inverse vs. Direct Variation Functions
Name that Parent Function
100
What is 128 to the 2/7 power as a radical?
7th root of 128 squared.
100
What are the Asymptotes for the following function 1/(x-3) + 4?
Vertical x=3 and Horizontal y=4.
100
What does x^7*x^5 =?
x^12
100
Draw a quick sketch of a possible inverse variation function.
Two hyperbolas, i.e. 1/x or 2/x
100
What is the parent function for the following function: -1/(x+2) - 5?
1/x
200
What is 64 to the .5 power?
The square Root of 64.
200
What are the Domain and Range of the following function 2/(x+3) - 5?
Domain: x is all real numbers except -3. Range: y is all real numbers except -5.
200
What does x^5/x^6 = ?
x^-1 or 1/x
200
Draw a quick sketch of a direct variation function.
a line i.e. 2x or 10x or any line going through the origin
200
What is the parent function for the following function: x^1/2 +3?
x^1/2 or the second radical of x
300
What is 3 to the -1 power using positive exponents only?
1/3
300
Where is the following function -3/x + 4 increasing and/or decreasing?
Increasing (-Infinity, 0) union (0, +infinity) Decreasing N/A we would use a circle with a line through it to show this. Remember, we look at the x-values for the Domain and Range, see when the function is increasing or decreasing from left to right!!
300
What does (2x^6y^2)^3 = ?
8 x^18 y^6
300
Determine whether the following function could be data from an inverse or direct variation function or neither. If so, give the function in the form of f(x)=k/x or f(x)=kx, or state neither. x 1.2 2.3 3.4 .54 -1.6 y 3.2 5.4 3.2 .36 -0.3
Neither, there are no patterns between the x and y data values.
300
What is the parent function for the following function: 1/(x+2)^2 + 6?
1/(x^2) or x^-2
400
Simplify 32^2/5.
4 b/c 32^2/5 = the 5th root of 32 to the 2nd power.
400
Describe the end behavior of the following function 1/(x+2) - 5.
As x approaches - infinity the function approaches -5, as x approaches + infinity the function approaches -5.
400
What does (5x^6)/(15x^3y^5) = ?
(x^3)/(3y^5) or 1/3 x^3y^-5
400
Determine whether the following function could be data from an inverse or direct variation function or neither. If so, give the function in the form of f(x)=k/x or f(x)=kx, or state neither. x 0.85 -0.59 -4.1 -1.4 y 2.295 -1.593 -11.07 -3.78
This is an direct variation function of the form y=2.7x
400
What is the graph of x^354 most like? a. quadratic function b. cubic function c. a linear function d. the absolute value function
A Quadratic Function because of the even exponent (Hint: x^2, x^4, etc are all quadratic functions(parabolas).)
500
Simplify the cube root of 64a^6b^7c^12
What is 4a^2b^2c^4 times the cube root of b
500
If the function has a vertical asymptote of x=-3 and a horizontal asymptote of y=4, and two corner points on each curve, what is a possible equation for this function?
2/(x+3) + 4, any number can be used above except 1 b/c 1/x only has one corner point on each curve.
500
What does {(3x^6y^4)^3}/{4x^3y^2}^2 = ?
{27x^12y^8}/16
500
Determine whether the following function could be data from an inverse or direct variation function or neither. If so, give the function in the form of f(x)=k/x or f(x)=kx, or state neither. x -3.2 0.55 2 -0.2 11 y 0.275 -1.6 -.44 4.40 -0.08
This is an inverse variation function of the form y = -0.88/x
500
What is the graph of x^1027 most like? a. a quadratic function b. an inverse variation function c. a cubic function d. a linear function
A Cubic Function because of the odd exponent. (Hint: x^3, x^5, etc are all cubic functions)