All Advanced Geometry Resources
Example Questions
Example Question #141 : Coordinate Geometry
Determine the y-intercept for the below function.
To determine the y-intercept for any function, we must plug in zero for x.
Everywhere there is an x, replace it with a 0.
When we simiplify we get:
This corresponds to the below ordered pair.
Example Question #142 : Coordinate Geometry
We can find the answer by plugging in the different coordinate pairs to test them.
Since this coordinate pair shows equality on both sides, we know it must be the answer.
Example Question #21 : How To Graph A Function
True or false: The graph of has as a horizontal asymptote the line of the equation .
False
True
False
is a rational function whose numerator has degree greater than that of its denominator (2 and 1, respectively). The graph of such a function does not have a horizontal asymptote.
Example Question #22 : How To Graph A Function
True or false: The graph of has as a horizontal asymptote the graph of the equation .
False
True
True
is a rational function whose numerator and denominator have the same degree (1). As such, it has as a horizontal asymptote the line of the equation , where is the quotient of the coefficients of the highest-degree terms of its numerator and denominator. Consequently, the horizontal asymptote of the graph of the equation
is the line of the equation
,
or
.
Example Question #23 : How To Graph A Function
True or false: The graph of has as a horizontal asymptote the graph of the equation .
False
True
False
is a rational function whose numerator and denominator have the same degree (1). As such, it has as a horizontal asymptote the line of the equation , where is the quotient of the coefficients of the highest-degree terms of its numerator and denominator. Consequently, the horizontal asymptote of the graph of the equation
is the line of the equation
.
Example Question #24 : How To Graph A Function
True or false: The graph of has as a horizontal asymptote the graph of the equation .
False
True
True
is a rational function whose numerator and denominator have the same degree (2). As such, it has as a horizontal asymptote the line of the equation , where is the quotient of the coefficients of the highest-degree terms of its numerator and denominator. Consequently, the horizontal asymptote of
is the line of the equation
, or
Example Question #147 : Coordinate Geometry
True or false: The graph of has as a vertical asymptote the graph of the equation .
True
False
False
The vertical asymptote(s) of the graph of a rational function such as can be found by evaluating the zeroes of the denominator after the rational expression is reduced. Here, set up and solve the linear equation
The graph of has the line of the equation as its only vertical asymptote.
Example Question #148 : Coordinate Geometry
Which of the following are the equations of the vertical asymptotes of the graph of ?
(a)
(b)
(c)
(a) only
All of (a), (b), and (c)
(a) and (b) only
None of (a), (b), and (c)
(c) only
None of (a), (b), and (c)
The vertical asymptote(s) of the graph of a rational function such as can be found by evaluating the zeroes of the denominator after the rational expression is reduced.
First, factor the numerator. It is a quadratic trinomial with lead term , so look to "reverse-FOIL" it as
by finding two integers with sum 6 and product 5. By trial and error, these integers can be found to be 1 and 5, so
Therefore, can be rewritten as
Set the denominator equal to 0 and solve for :
By the Zero Factor Principle,
or
Therefore, the graph of has as its two vertical asymptotes the lines of the equations and , neither of which are among the choices given.
Example Question #149 : Coordinate Geometry
Give the domain of the function
.
The set of all real numbers
As a rational function, has as its domain the set of all values for which the denominator is not equal to 0. Solve the equation:
The domain excludes only the value - that is, the domain is .
Example Question #31 : How To Graph A Function
Give the domain of the function
The set of all real numbers
The square root of a real number is defined only for nonnegative radicands; therefore, the domain of is exactly those values for which the radicand is nonnegative. Solve the inequality:
The domain of is .