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Begin Game
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Function Basics
One to One fun
Graphing Functions
Max and Min
Anything Goes
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Function Basics
Main Board Answer
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Evaluate the function at the give value
The answer is:
Main Board Question
Function Basics $ 100
Function BasicsGiven that this is the graph of f(x), what is the
value of f(-2)
Main Board Answer
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The answer is: f(-2)=1
Main Board Question
Function Basics $ 200
Function Basics
Given how h(x) and z(x) are defined, find the following
Main Board Answer
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The answer is:
Main Board Question
Function Basics $ 300
Function Basics
Find the average rate of change of the function between the given values.
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The answer is:
Main Board Question
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Function Basics
What is the domain:
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The answer is:
Main Board Question
Function Basics $ 500
One to One fun
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Given that
Find
Main Board Question
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One to One fun
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In order to find an inverse for a function, we first make sure the function is _______.
If we have the graph of the function, this comes down to using the _________ line test.
Main Board Question
One to One fun $ 200
In order to find an inverse for a function, we first make sure the function is one-to-one.
If we have the graph of the function, this comes down to using the horizontal line test.
One to One fun
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Find the inverse of the following function
Main Board Question
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One to One fun
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How could you describe the graph of f(x) when it is compared to the graph of the
inverse of f(x)?
Main Board Question
One to One fun $ 400
They are reflections of one another over the line y = x.
One to One fun
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When give two functions say h(x) and g(x), how can you determine if they are inverses of
one another.
Main Board Question
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If you have the graphs of h(x) and g(x), you can check if they are reflections of one
another over the y = x line.
If you have the equations of h(x) and g(x), then you must compute h(g(x)) and g(h(x)), and show that both of these are equal to x
Graphing Functions
Graph f(x)
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The answer is:
Main Board Question
$ 100Graphing Functions
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Write f(x) in standard form. Graph f(x)
Graphing Functions
Main Board Question
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The answer is:
Graphing Functions
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List all the transformation in the function, and what caused the transformation.
y = -f(9x) + 3
Graphing Functions
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•The negative sign out front reflects f(x) in the x-axis (pg 185)
•The 9 in the function shrinks f(x) by a factor of 1/9 (pg 187)
•The 3 outside the function shifts f(x) up 3 units (pg 183)
Graphing Functions
Main Board Answer
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Given the graph of g(x) below, graph
y = 4g(x - 1)
Graphing Functions
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The answer is:
Graphing Functions
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What is the “parent” function below. How has it been transformed? Write the function
Graphing Functions
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The parent function is:
It has been shifted to the right 4, and down 2:
Graphing Functions
Find the maximum or minimum of the following function
Main Board Answer
$ 100Max and Min
The minimum occurs at the vertex, which is
(-2, -3)
Main Board Question
$ 100Max and Min
What is the maximum value of f(x)
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$ 200Max and Min
Complete the square to get it into standard form. The minimum occurs at (-2,-10)
Main Board Question
$ 200Max and Min
For what intervals is f(x) increasing, and decreasing?
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$ 300Max and Min
The answer is:
Main Board Question
$ 300Max and Min
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A projectile on Earth is fired straight upward so that its distance (in feet) above the ground t
seconds after firing is given by
Find the maximum height it reaches and the number of seconds it takes to reach that
height.
Max and Min
We use the formula on pg 197 to get that the maximum height will be reached after 12.5
seconds.
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We plug this into the function to get that the maximum height will be 2500 ft.
Max and Min
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If 1800 ft of fencing is available to build five adjacent pens as shown in the diagram, What are the dimensions, and maximum area of all
the pens?
Max and Min
The function that models the area will be
Main Board Question
Max and Min $ 500
Where x is the width of the pens. Using the formula on pg 197 we get the area will be
maximized when x = 150 ft.
Using this we can find that the maximum area will be 67500 square feet.
Anything Goes
State the vertical line test. What is it used for?
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A curve in the coordinate plane is a graph of a function if and only if no vertical line intersects
the curve more than once. Pg 163
We use this test when we have a graph and we want to determine if it’s a function or not.
Main Board Question
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Anything Goes
What is the domain of f(x)/g(x)
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This is the domain of f(x) intersected with the domain of g(x), not including those places
where g(x) is equal zero.
For more precise notation on the domain and an example see Pg 214-215.
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Anything Goes
If f(x) is given by the following
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Find the value of
The answer is:
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Anything Goes $ 300
Anything Goes
Find a function that models the length of a rectangle in terms of its perimeter and width
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This is a function for perimeter in terms of length and width
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Anything Goes $ 400
To get a function that models length in terms of perimeter and width, we solve for l.
Anything Goes
Graph the greatest integer function.
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Can we apply transformations to this function?
Is this function one-to-one?
This can be found on pg 166.
Main Board Question
Anything Goes $ 500
Even though this function looks very different from the other functions we have covered, we can apply transformations to it as well. It is not one-to-one since it doesn’t pass the horizontal line test.
