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Function Basics
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Evaluate the function at the give value
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Function Basics
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The answer is:
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Function Basics
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Given that this is the graph of f(x), what is the
value of f(-2)
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Function Basics
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The answer is: f(-2)=1
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Function Basics
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Given how h(x) and z(x) are defined, find the
following
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Function Basics
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The answer is:
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Function Basics
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Find the average rate of change of the
function between the given values.
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Function Basics
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The answer is:
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Function Basics
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What is the domain:
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Function Basics
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The answer is:
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One to One fun
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Given that
Find
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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.
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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.
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One to One fun
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Find the inverse of the following function
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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)?
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They are reflections of one another over the
line y = x.
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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.
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One to One fun
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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
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Graphing Functions
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Graph f(x)
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Graphing Functions
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The answer is:
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Graphing Functions
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Write f(x) in standard form. Graph f(x)
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Graphing Functions
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The answer is:
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Graphing Functions
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List all the transformation in the function, and
what caused the transformation.
y = -f(9x) + 3
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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)
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Graphing Functions
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Given the graph of g(x) below, graph
y = 4g(x - 1)
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Graphing Functions
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The answer is:
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Graphing Functions
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What is the “parent” function below. How has
it been transformed? Write the function
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Graphing Functions
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The parent function is:
It has been shifted to the right 4, and down 2:
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Max and Min
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Find the maximum or minimum of the
following function
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Max and Min
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The minimum occurs at the vertex, which is
(-2, -3)
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Max and Min
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What is the maximum value of f(x)
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Max and Min
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Complete the square to get it into standard
form. The minimum occurs at (-2,-10)
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For what intervals is f(x) increasing, and
decreasing?
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The answer is:
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Max 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.
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Max and Min
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We use the formula on pg 197 to get that the
maximum height will be reached after 12.5
seconds.
We plug this into the function to get that the
maximum height will be 2500 ft.
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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?
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The function that models the area will be
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.
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Anything Goes
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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.
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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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If f(x) is given by the following
Find the value of
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The answer is:
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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
To get a function that models length in terms
of perimeter and width, we solve for l.
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Anything Goes
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Graph the greatest integer function.
Can we apply transformations to this function?
Is this function one-to-one?
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This can be found on pg 166.
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-toone since it doesn’t pass the horizontal line test.
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