All Precalculus Resources
Example Questions
Example Question #14 : Relations And Functions
Finding an inverse function.
Given
find
.
.
.
Finding an inverse function is essentially finding the output in terms of the input. To do this switch the independent and dependent variables. First set
.
Then
Now, to switch the role of the variables solve for x in terms of y.
or
So, y is now the independent variable, and x is the dependent variable. The final step is to write the inverse function in proper notation.
Set , and .
This gives
.
Example Question #15 : Relations And Functions
Which function below correctly translates four units to the right and two units down?
The translation moves the graph of units to the left if . To see this, compare the graphs of and . A translation to the right must be in the form if .
A vertical translation is up if . We want to move the function down, so our translation subtracts two from .
Combining these, we get .
Example Question #51 : Pre Calculus
What is the domain of the following function?

The denominator becomes zero whenever cos(x) becomes 1 and this happens when x is an odd multiple of . To avoid division by zero, we exclude all these numbers. Therefore the domain is:
Example Question #2 : Angles
The angles are supplementary, therefore, the sum of the angles must equal .
Example Question #7 : Angles
Are and supplementary angles?
No
Yes
Not enough information
Yes
Since supplementary angles must add up to , the given angles are indeed supplementary.
Example Question #1 : Angles
The angles containing the variable all reside along one line, therefore, their sum must be .
Because and are opposite angles, they must be equal.
Example Question #1 : Graphs Of Polynomial Functions
For what values of will the given polynomial pass through the xaxis if plotted in Cartesian coordinates?
None of the other answers
One can remember that if the multiplicity of a zero is odd then it passes through the xaxis and if it's even then it 'bounces' off the xaxis. You can think about this analytically as well. What happens when we plug a number into our function just slightly above or below a zero with an even multiplicity? You find that the sign is always positive. Whereas a zero with an odd multiplicity will yield a positive on one side and a negative on the other. For zeros with odd multiplicity this alters the sign of our output and the function passes through the xaxis. Whereas the zero with even multiplicity will output a number with the same sign just above and below its zero, thus it 'bounces' off the xaxis.
Example Question #2 : Graphs Of Polynomial Functions
For this particular question we are restricting the domain of both to nonnegative values, or the interval .
Let and .
For what values of is ?
The cubic function will increase more quickly than the quadratic, so the quadratic function must have a head start. At , both functions evaluate to 8. After than point, the cubic function will increase more quickly.
The domain was restricted to nonnegative values, so this interval is our only answer.
Example Question #51 : Pre Calculus
What is the ?
Example Question #2 : Graphs And Inverses Of Trigonometric Functions
In the right triangle above, which of the following expressions gives the length of y?
is defined as the ratio of the adjacent side to the hypotenuse, or in this case . Solving for y gives the correct expression.
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