Chapter 2- domain, range, piecewise functions, inverse functions, concavity, qua
Terms
undefined, object
copy deck
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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?
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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
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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?
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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
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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?
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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.
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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 - true