How to graph an exponential function - ACT Math
Card 0 of 54
If the functions


were graphed on the same coordinate axes, what would be the
-coordinate of their point of intersection?
Round to the nearest tenth, if applicable.
If the functions
were graphed on the same coordinate axes, what would be the -coordinate of their point of intersection?
Round to the nearest tenth, if applicable.
We can rewrite the statements using
for both
and
as follows:


To solve this, we can set the expressions equal, as follows:






We can rewrite the statements using for both
and
as follows:
To solve this, we can set the expressions equal, as follows:
Compare your answer with the correct one above
If the functions


were graphed on the same coordinate axes, what would be the
-coordinate of their point of intersection?
Round to the nearest tenth, if applicable.
If the functions
were graphed on the same coordinate axes, what would be the -coordinate of their point of intersection?
Round to the nearest tenth, if applicable.
We can rewrite the statements using
for both
and
as follows:


To solve this, we can multiply the first equation by
, then add:





We can rewrite the statements using for both
and
as follows:
To solve this, we can multiply the first equation by , then add:
Compare your answer with the correct one above
Give the
-intercept of the graph of the function

Round to the nearest tenth, if applicable.
Give the -intercept of the graph of the function
Round to the nearest tenth, if applicable.
The
-intercept is
, where
:











The
-intercept is
.
The -intercept is
, where
:
The -intercept is
.
Compare your answer with the correct one above
Give the
-intercept of the graph of the function

Round to the nearest hundredth, if applicable.
Give the -intercept of the graph of the function
Round to the nearest hundredth, if applicable.
The
-intercept is
:






is the
-intercept.
The -intercept is
:
is the
-intercept.
Compare your answer with the correct one above
Give the horizontal asymptote of the graph of the function

Give the horizontal asymptote of the graph of the function
We can rewrite this as follows:



This is a translation of the graph of
, which has
as its horizontal asymptote, to the right two units and down three units. Because of the latter translation, the horizontal asymptote is
.
We can rewrite this as follows:
This is a translation of the graph of , which has
as its horizontal asymptote, to the right two units and down three units. Because of the latter translation, the horizontal asymptote is
.
Compare your answer with the correct one above
Give the vertical asymptote of the graph of the function

Give the vertical asymptote of the graph of the function
Since 4 can be raised to the power of any real number, the domain of
is the set of all real numbers. Therefore, there is no vertical asymptote of the graph of
.
Since 4 can be raised to the power of any real number, the domain of is the set of all real numbers. Therefore, there is no vertical asymptote of the graph of
.
Compare your answer with the correct one above
If the functions


were graphed on the same coordinate axes, what would be the
-coordinate of their point of intersection?
Round to the nearest tenth, if applicable.
If the functions
were graphed on the same coordinate axes, what would be the -coordinate of their point of intersection?
Round to the nearest tenth, if applicable.
We can rewrite the statements using
for both
and
as follows:


To solve this, we can set the expressions equal, as follows:






We can rewrite the statements using for both
and
as follows:
To solve this, we can set the expressions equal, as follows:
Compare your answer with the correct one above
If the functions


were graphed on the same coordinate axes, what would be the
-coordinate of their point of intersection?
Round to the nearest tenth, if applicable.
If the functions
were graphed on the same coordinate axes, what would be the -coordinate of their point of intersection?
Round to the nearest tenth, if applicable.
We can rewrite the statements using
for both
and
as follows:


To solve this, we can multiply the first equation by
, then add:





We can rewrite the statements using for both
and
as follows:
To solve this, we can multiply the first equation by , then add:
Compare your answer with the correct one above
Give the
-intercept of the graph of the function

Round to the nearest tenth, if applicable.
Give the -intercept of the graph of the function
Round to the nearest tenth, if applicable.
The
-intercept is
, where
:











The
-intercept is
.
The -intercept is
, where
:
The -intercept is
.
Compare your answer with the correct one above
Give the
-intercept of the graph of the function

Round to the nearest hundredth, if applicable.
Give the -intercept of the graph of the function
Round to the nearest hundredth, if applicable.
The
-intercept is
:






is the
-intercept.
The -intercept is
:
is the
-intercept.
Compare your answer with the correct one above
Give the horizontal asymptote of the graph of the function

Give the horizontal asymptote of the graph of the function
We can rewrite this as follows:



This is a translation of the graph of
, which has
as its horizontal asymptote, to the right two units and down three units. Because of the latter translation, the horizontal asymptote is
.
We can rewrite this as follows:
This is a translation of the graph of , which has
as its horizontal asymptote, to the right two units and down three units. Because of the latter translation, the horizontal asymptote is
.
Compare your answer with the correct one above
Give the vertical asymptote of the graph of the function

Give the vertical asymptote of the graph of the function
Since 4 can be raised to the power of any real number, the domain of
is the set of all real numbers. Therefore, there is no vertical asymptote of the graph of
.
Since 4 can be raised to the power of any real number, the domain of is the set of all real numbers. Therefore, there is no vertical asymptote of the graph of
.
Compare your answer with the correct one above
If the functions


were graphed on the same coordinate axes, what would be the
-coordinate of their point of intersection?
Round to the nearest tenth, if applicable.
If the functions
were graphed on the same coordinate axes, what would be the -coordinate of their point of intersection?
Round to the nearest tenth, if applicable.
We can rewrite the statements using
for both
and
as follows:


To solve this, we can set the expressions equal, as follows:






We can rewrite the statements using for both
and
as follows:
To solve this, we can set the expressions equal, as follows:
Compare your answer with the correct one above
If the functions


were graphed on the same coordinate axes, what would be the
-coordinate of their point of intersection?
Round to the nearest tenth, if applicable.
If the functions
were graphed on the same coordinate axes, what would be the -coordinate of their point of intersection?
Round to the nearest tenth, if applicable.
We can rewrite the statements using
for both
and
as follows:


To solve this, we can multiply the first equation by
, then add:





We can rewrite the statements using for both
and
as follows:
To solve this, we can multiply the first equation by , then add:
Compare your answer with the correct one above
Give the
-intercept of the graph of the function

Round to the nearest tenth, if applicable.
Give the -intercept of the graph of the function
Round to the nearest tenth, if applicable.
The
-intercept is
, where
:











The
-intercept is
.
The -intercept is
, where
:
The -intercept is
.
Compare your answer with the correct one above
Give the
-intercept of the graph of the function

Round to the nearest hundredth, if applicable.
Give the -intercept of the graph of the function
Round to the nearest hundredth, if applicable.
The
-intercept is
:






is the
-intercept.
The -intercept is
:
is the
-intercept.
Compare your answer with the correct one above
Give the horizontal asymptote of the graph of the function

Give the horizontal asymptote of the graph of the function
We can rewrite this as follows:



This is a translation of the graph of
, which has
as its horizontal asymptote, to the right two units and down three units. Because of the latter translation, the horizontal asymptote is
.
We can rewrite this as follows:
This is a translation of the graph of , which has
as its horizontal asymptote, to the right two units and down three units. Because of the latter translation, the horizontal asymptote is
.
Compare your answer with the correct one above
Give the vertical asymptote of the graph of the function

Give the vertical asymptote of the graph of the function
Since 4 can be raised to the power of any real number, the domain of
is the set of all real numbers. Therefore, there is no vertical asymptote of the graph of
.
Since 4 can be raised to the power of any real number, the domain of is the set of all real numbers. Therefore, there is no vertical asymptote of the graph of
.
Compare your answer with the correct one above
If the functions


were graphed on the same coordinate axes, what would be the
-coordinate of their point of intersection?
Round to the nearest tenth, if applicable.
If the functions
were graphed on the same coordinate axes, what would be the -coordinate of their point of intersection?
Round to the nearest tenth, if applicable.
We can rewrite the statements using
for both
and
as follows:


To solve this, we can set the expressions equal, as follows:






We can rewrite the statements using for both
and
as follows:
To solve this, we can set the expressions equal, as follows:
Compare your answer with the correct one above
If the functions


were graphed on the same coordinate axes, what would be the
-coordinate of their point of intersection?
Round to the nearest tenth, if applicable.
If the functions
were graphed on the same coordinate axes, what would be the -coordinate of their point of intersection?
Round to the nearest tenth, if applicable.
We can rewrite the statements using
for both
and
as follows:


To solve this, we can multiply the first equation by
, then add:





We can rewrite the statements using for both
and
as follows:
To solve this, we can multiply the first equation by , then add:
Compare your answer with the correct one above