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### 15 Cards in this Set

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 if f(x)= (x^3+5)/20 solve f(x)=4 4=(x^3 + 5)/20 80=x^3 + 5 75=x^3 75^(1/3)=(x^3)^(1/3) 75^(1/3)=x The domain is the set of ________ while the range is the set of ________ inputs; outputs What type of function has different formulas on different intervals? Piecewise functions if y=f(x) then what are the input and outputs of f inverse? input=y output=x If you are given a formula for y=f(x), how do you find the inverse formula? solve the formula for x. What ever x equals, this is the inverse formula. How is concavity related to a function? The concavity of a function tells you if the RATE OF CHANGE of the function is INCREASING OR DECREASING A function that is concave up has an __________ rate of change while a function that is concave down has a ___________ rate of change increasing, decreasing What is the standard form of a quadratic function? ax^2 +bx +c what is the factored form of a quadratic function? a(x-r)(x-s) where r and s are roots of the function. What is the quadratic formula used for and what is the formula? Used to solve for the roots of an equation. x=[-b +/- sqrt(b^2-4ac)]/(2a) true or false If f(3)=5 and f is invertible then finverse(5)=3 true True or false a function can be both increasing and concave down true, consider log(x) or ln(x) If a table has points (-2,5), (0,6), (2,8), (4,12), is the graph concave up, down or neither? compare the rates of change for each interval and see if they are increasing,decreasing or neither: interval 1: (5-6)/(-2-0) = 1/2 interval 2: (6-8)/(0-2) = 1 interval 3: (8-12)/(2-4)= 2 since 1/2<1<2 the slope is increasing from left to right so the function is concave up. If the height above the ground of an object at time t is given by s(t)=a(t^2) +bt + c, then s(0) tells us what? the height above the ground of the object at time t=zero. True or false To solve a quadratic equation, one should get all the terms to one side and zero on the other side, then find the zeros of the function. To solve a linear function, one should try to get x on one side and all the other terms on the other true