It is the domain and range of the equation f(x)=(x–5)^3 –5 in interval notation
What is:
(-∞,∞) for the domain
and [-5,∞) for the range
100
It is the line that relates the graphs of f(x) and its inverse
What is the line y=x
100
It is the effect of 'a' in the function a*f(x)
What is a vertical dilation
If a>1 the function is stretched
If 0>a>1 the function is squeezed
100
It is the value of (4^4 * 5^5)^3
What is 4^12 * 5^15
100
It is the exponential equivalent for log(12,144)=2
What is 12^2 = 144
200
It is the domain, range, and asymptote of f(x) = 2^x + 2
What is:
all real numbers for the domain
(2, ∞) for the range
and y = 2 for the asymptote
200
It is the point that corresponds with (16,-3) on the graph’s inverse
What is (-3,16)
200
It is the general relation of the graph f(x)=(x)^2 to the graph f(x)=(x-b)^2
What is the graph of f(x)=x^2 shifted horizontally by the value of b
If b is negative, the shift is to the left
If b is positive the graph shifts to the right
200
It is the proof that justifies that a^m * a^n = a^(m+n)
What is the rule that the product of 'a' multiplied by itself 'm' times and 'a' multiplied by itself 'n' times is the same as saying 'a' multiplied by itself 'm' plus 'n' times
200
It is the value of x when 10^x = 21
What is log(10,21)
x = 1.322219295
300
It is the value of g(f(x)) when x=7 given that g(x)=x–1 and f(x)=3x–5
What is 15
300
It is the condition or rule that allows f(x) = x^3 to have an inverse while f(x) = x^2 does not
What is one-to-one — the graph must pass the horizontal line test
300
It is the new zeroes of y=f(x–4) when the zeroes of the original function are -4, 1, and 7
What is 0, 5, and 11
300
It is a simplified expression of ((4a^2)^3)/16a^3
What is 4a^3
300
It is the relationship between f(x)=10^x and f(x)=log(x)
What is an inverse relationship
400
It is the domain of g(x) = ½f(x/2) given the domain of f(x) is [-6,10]
What is [-12,20]
400
It is the inverse of f(x)=1/2x+4
What is 2x – 4
400
It is the equation of the function f(x)=x^2 reflected over the x-axis, stretched vertically be a factor of 2, shifted left 3 and up 7
What is f(x)=-2(x+3)^2+7
400
It is the value of x when 8^(4x+1) = 2^(6x+9)
What is -2
400
It is an equivalent to log(10,16) written as a sum of two other logs
What is log(10,8) + log(10,2)
500
It is the value of g(x) when
f(x) = (x–2)
and g(f(x)) = 2(x–2)^2 +1
What is 2(x)^2 +1
500
It is the inverse of the function f(x) = (x–2)^1/2 – 2
What is (x+2)^2 + 2
500
It is the equation of the function f(x)=2^x reflected over the y-axis and down 3
What is f(x)=2^(-x) -3
500
It is the value of a and b in the function f(x) =a*b^x
given that:
f(3) = 12
and
f(4) = 16
What is
a = 81/16
and
b = 4/3
500
It is the reason why log(10,-5) cannot be evaluated
What is the logarithmic rule that states that b^x=y and log(b,y)=x and because of that, no number raised to any x power can equal a negative y value