All GMAT Math Resources
Example Questions
Example Question #1 :Graphing
Give the-intercept(s) of the graph of the equation
The graph has no-intercept.
Setand solve for:
Example Question #1 :Graphing An Exponential Function
Define a functionas follows:
Give the-intercept of the graph of.
The graph ofhas no-intercept.
The graph ofhas no-intercept.
Since the-intercept is the point at which the graph ofintersects the-axis, the-coordinate is 0, and the-coordinate can be found by settingequal to 0 and solving for. Therefore, we need to findsuch that. However, any power of a positive number must be positive, sofor all real, andhas no real solution. The graph oftherefore has no-intercept.
Example Question #1 :How To Graph An Exponential Function
Define a functionas follows:
Give the vertical aysmptote of the graph of.
The graph ofdoes not have a vertical asymptote.
The graph ofdoes not have a vertical asymptote.
Since any number, positive or negative, can appear as an exponent, the domain of the functionis the set of all real numbers; in other words,is defined for all real values of. It is therefore impossible for the graph to have a vertical asymptote.
Example Question #981 :Problem Solving Questions
Define a functionas follows:
Give the-intercept of the graph of.
The graph ofhas no-intercept.
Since the-intercept is the point at which the graph ofintersects the-axis, the-coordinate is 0, and the-coordinate can be found by settingequal to 0 and solving for. Therefore, we need to findsuch that
.
The-intercept is therefore.
Example Question #5 :How To Graph An Exponential Function
Define a functionas follows:
Give the horizontal aysmptote of the graph of.
The horizontal asymptote of an exponential function can be found by noting that a positive number raised to any power must be positive. Therefore,andfor all real values of. The graph will never crosst the line of the equatin, so this is the horizontal asymptote.
Example Question #6 :How To Graph An Exponential Function
Define functionsandas follows:
Give the-coordinate of the point of intersection of their graphs.
First, we rewrite both functions with a common base:
is left as it is.
can be rewritten as
To find the point of intersection of the graphs of the functions, set
The powers are equal and the bases are equal, so we can set the exponents equal to each other and solve:
To find the-coordinate, substitute 4 forin either definition:
, the correct response.
Example Question #133 :Exponential And Logarithmic Functions
Define a functionas follows:
Give the-intercept of the graph of.
The-coordinate ofthe-intercept of the graph ofis 0, and its-coordinate is:
The-intercept is the point.
Example Question #7 :How To Graph An Exponential Function
Define functionsandas follows:
Give the-coordinate of the point of intersection of their graphs.
First, we rewrite both functions with a common base:
is left as it is.
can be rewritten as
To find the point of intersection of the graphs of the functions, set
Since the powers of the same base are equal, we can set the exponents equal:
Now substitute in either function:
, the correct answer.
Example Question #1 :Graphing
Define a functionas follows:
Give the-intercept of the graph of.
Since the-intercept is the point at which the graph ofintersects the-axis, the-coordinate is 0, and the-coordinate is:
,
The-intercept is the point.
Example Question #9 :How To Graph An Exponential Function
Evaluate.
The system has no solution.
Rewrite the system as
and substituteandforand, respectively, to form the system
Add both sides:
.
Now backsolve:
Now substitute back:
and