Functions:
Functions: Transformations
Exponents
Logarithms
Geometry
100
The x and y intercepts of y=-2log(5,((1/3)x+5)-4).
What is (-14.88,0) and (0,-6)?
100
f(x) = 2(x+4)^2
What is the equation of the quadratic function shifted 4 units to the left and stretched vertically by a factor of 2?
100
The simplified version of the expression -5n(-5n^-2)^-1.
What is n^3?
100
log((6*x^4)/y^3))
What is log(6)+4log(x)-3log(y) written as a single logarithm?
100
An angle that measures 143°
What is the the supplement of a 37° angle?
200
A quadratic function has the domain of all real numbers, the range of y≤0, has been stretched by a factor of 2, and has been shifted left three units.
What are some properties the equation y=-2(x+3)^2
200
f(x)=-(x-15)^3
What is the equation of the cubic function shifted 15 units to the right and reflected across the x-axis?
200
What is 1/(125v^3) written exponentially?
(5v)^-3
200
4^(2x+9)=20^(-x-4). Find the value of x.
x=-3.28
200
Johnny works in a two story building that is 400ft by 100ft. He wants to build a triangular pool that has a base of 28ft and a height of 56ft in the center of the first floor. How much of the building would be left for office space?
79,216ft^2
300
The asymptote of the graph y=log(3,-2x+7)-3.
What is x=-7?
300
f(x)=-2x
What is the equation of linear function compressed horizontally by a factor of 2 and reflected over the x-axis?
300
[(3x4y7z12)^5+(–5x9y3z4)^2]0. solve
1
300
Y=(10^(x+7)+3)/2
What is f^-1(x) if f(x) is -log (2x-3)+7?
300
Two circles are concentric. The radius of the large circle is 10 and that of the small circle is 6. The endpoints of cord AB are on the large circle and the midpoint is on the small circle. What is the length of the cord AB?
16. (Pythagorean theorem)
400
The equation of a parabola with a vertex of (2,4) and a y-intercept of (0,-3) restricted to be one-to-one.
What is Equation f(x)=-(7/4)((x-2)^2)+4 with a restricted domain of x≥2 or to x≤2?
400
1. vertical shift(up/down) 2. reflect across x-axis 3. vertical stretch/compress 4. reflect across y-axis. 5. horizontal stretch/compress 6. horizontal shift(left/right)
What is the order of transformations backwards?
400
x^(2/3) is equal to ∛(x^2).
What is an example of the fractional exponents law?
400
The value of a diamond increases by 9.5% each year. Find how many years it will take 1 gram to be worth $10,000 if 1 gram is worth $7,000 today.
3.94 years
400
Three times the width of a certain rectangle exceeds twice its length by three inches, and four times its length is twelve more than its perimeter. Find the dimensions of the rectangle.
The length is 21" and the width is 15"
500
This symbol is created when you do the following: Graph the cubic function with a restricted domain of -7≤x≤7 and a restricted range of -7≤y≤7. On the same axis, draw a circle with a radius of 7 and a center at the origin. Draw two small circles, one around the point (1, -3) and the other around the the point (-1,3), each with a radius of one. Erase anything outside of the circle large circle.
What is the yin-yang symbol?
500
The exponential function vertically reflected, vertically stretched by 3, and vertically translated down 10.
What is y=-3((2)^x)-10?
500
3^(x+2)-3^x=6^3(3^7). Solve for x.
= 3^x(3^2-1)=216(3^7) =3^x(8)=216(3^7) =3^x=27(3^7) =3^(x-7)=27 3^3=27 x=10
500
If log(b,a)=10, log(b,c)=5, and log(b,d)=2, then what is log (b, (c^2*d^3)/(a*b^2))?
4
500
points A, B, C and D are on a circle. Point O is the intersection of chords AC and BD. The area of triangle BOC is 15; the length of AO is 10 and the length of OB is 5. What is the area of triangle AOD?
AOD is 4 times the area of triangle BOC and is equal to 60.
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