Download - Chapter 3 Review Pre-Calculus
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Chapter 3 Review
Pre-Calculus
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Determine what each graph is symmetric with respect to
y-axis y-axis, x-axis, origin, y = x, and y = -x
y-axis, x-axis, and origin
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The graph of each equation is symmetric with respect to what?
Two squared terms, with same coefficients means it is an circle with center (0, 0)
Symmetric with respect to x-axis, y-axis, origin, y = x, and y = -x
Two squared terms, but different coefficients means it is an ellipse with center (0, 0)
Symmetric with respect to x-axis, y-axis, and origin
One squared term means it is a parabola shifted up 5 units and more narrow.
Symmetric with respect to the y-axis
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Graph each equation:
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Graph each equation:
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Determine whether each function is even, odd or neither.
If all the signs are opposite, then the function is EVEN
Figure out f(-x) and –f(x)
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Determine whether each function is even, odd or neither.
If all the signs are opposite and the same, then the function is NEITHER even or odd.
Figure out f(-x) and –f(x)
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Determine whether each function is even, odd or neither.
If all the signs are the same,then it is ODD
Figure out f(-x) and –f(x)
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Describe the transformation that relates the graph of to the parent graph
THREE UNITS TO THE LEFT
Describe the transformation that relates the graph of to the parent graph
THREE UNITS UP, AND MORE NARROW
Describe the transformation that relates the graph of to the parent graph
FOUR UNITS TO THE RIGHT, AND THREE UNITS UP
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Describe the transformations that has taken place in each family graph.
Right 5 units
Up 3 units
More Narrow
More Narrow, and left 2 units
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Describe the transformations that has taken place in each family graph.
More Wide, and right 4 unitsRight 3 units, and up 10 units
More Narrow
Reflected over x-axis, and moved right 5 units
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Describe the transformations that has taken place in each family graph.
Reflect over x-axis, and up 2 units
Reflected over y-axis
Right 2 units
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FINDING INVERSE FINDING INVERSE FUNCTIONSFUNCTIONS
STEPS
Replace f (x) with y
Interchange the roles of x and y
Solve for y
Replace y with f -1(x)
Find the inverse of ,
y x 2
x y 2
x y2
y x
f 1(x) x , x 0
f (x) x 2
x 0
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FINDING INVERSE FINDING INVERSE FUNCTIONSFUNCTIONS
STEPS
Replace f (x) with y
Interchange the roles of x and y
Solve for y
Replace y with f -1(x)
Find the inverse of f (x) = 4x + 5
y 4x 5
x 4y 5
x 5 4y
x 54
y
f 1(x) x 5
4
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STEPS
Replace f (x) with y
Interchange the roles of x and y
Solve for y
Replace y with f -1(x)
Find the inverse of f (x) = 2x3 - 1
f 1(x) x 1
23
y 2x 3 1
x 2y 3 1
x 12y 3
x 1
2y 3
y x12
3
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STEPS
Replace f (x) with y
Interchange the roles of x and y
Solve for y
Replace y with f -1(x)
Find the inverse of
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Find the inverse of Steps for findingan inverse.
1. solve for x
2. exchange x’sand y’s
3. replace y with f-1
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Graph then function and it’s inverse of the same graph.
Parabola shifted 4 units left, and 1 unit down
Now to graph the inverse, just take each point and switch the x and y value and graph the new points.
Ex: (-4, -1) becomes (-1, -4)
Finally CHECK yourself by sketching the line y = x and make sure your graphs are symmetric with that line.
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Graph then function and it’s inverse of the same graph.
Cubic graph shifted 5 units to the left
Now to graph the inverse, just take each point and switch the x and y value and graph the new points.
Ex: (-5, 0) becomes (0, -5)
Finally CHECK yourself by sketching the line y = x and make sure your graphs are symmetric with that line.
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Graph then function and it’s inverse of the same graph.
Parabola shifted down 2 units
Now to graph the inverse, just take each point and switch the x and y value and graph the new points.
Ex: (0, -2) becomes (-2, 0)
Finally CHECK yourself by sketching the line y = x and make sure your graphs are symmetric with that line.
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x 2
f xx 2 x 2
Vertical Asymptotes: x 2Horizontal Asymptotes: y 0
Holes: 1
2,4
Intercepts:
1
x 2
10,
2
10,
2
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Determine if each parabola has a maximum value or a minimum value. y = ax2 + bx + c
“a” is positive so that means it opens up, and has a minimum
“a” is negative so that means it opens down, and has a maximum
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Graph each inequality:
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Find the maximum point of the graph of each:
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Find the x and y intercepts of
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Without graphing, describe the end behavior of the graph of
Positive coefficient, even power means it rises right and left
Negative coefficient, even power means it falls right and left
positive coefficient, odd power means it rises right and falls left
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Without graphing, describe the end behavior of the graph of
Positive coefficient, even power means it rises to left and falls to right
Positive coefficient, odd power means it rises right and falls left
positive coefficient, even power means it rises right and rises left
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Part Two
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Determine whether each function is even, odd, or neither.
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Graph the function Find the inverse equationGraph the inverse on the same graph. Is the inverse a function?
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Determine the asymptotes for the rational function then graph it
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Graph the inequality
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Find the derivative of the function
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Find the derivative of the function
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Find the equation of the tangent to
y = x3 + 2x at:
A.) x = 2 B.) x = -1
C.) x = -2
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f’(x)=0
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Step 1: Find the derivative, f’(x)
Step 2: Set derivative equal to zero and solve, f’(x)=0
Step 3: Plug solutions into original formula to find y-value, (solution, y-
value) is the coordinates.
Note: If it asks for the equation then you will write y=y value found when
you plugged in the solutions for f’(x)=0
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Determine three critical points that are found on the graph of .Identify each equation as a relative max, min, or point of inflection.
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Find the x and y intercept of
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Sketch the graph ofDescribe the graph.