QuestionSketch the graph of the function $y=3.2^{x+1}-1$ .

Studdy Solution

STEP 1

Assumptions1. The function is $y=3.^{x+1}-1$ . The function is an exponential function, as it is in the form $y=a^{x}$
3. The base of the exponential function is3.4. The function has been shifted1 unit to the left and1 unit down

STEP 2

First, we need to identify the key features of the graph. These include the y-intercept, the horizontal asymptote, and the general shape of the graph.
The y-intercept is the point where the graph crosses the y-axis. This occurs when $x=0$ . $y =.2^{0+1}-1$

STEP 3

Calculate the y-intercept by plugging in $x=0$ into the function.
$y =3.2^{1}-1$

STEP 4

Calculate the y-intercept.
$y =3.2-1 =2.2$ So the y-intercept is at (0,2.2).

STEP 5

The horizontal asymptote of an exponential function is usually at $y=0$ . However, since our function has been shifted down by1 unit, the horizontal asymptote will be at $y=-1$ .

STEP 6

The general shape of the graph of an exponential function $y=a^{x}$ , where $a>1$ , is that it increases as $x$ increases. Since our base is3.2, which is greater than1, our graph will also have this general shape.

STEP 7

Now, we can start sketching the graph. First, draw the horizontal asymptote at $y=-1$ .

STEP 8

Plot the y-intercept at (0,2.2).

STEP 9

Since the graph increases as $x$ increases, draw the graph so that it is getting closer to the horizontal asymptote as $x$ decreases and getting farther from the horizontal asymptote as $x$ increases.

STEP 10

Remember that the graph has been shifted unit to the left. This means that for any given $x$ , the corresponding $y$ value on our graph will be the $y$ value of $y=3.2^{x}$ shifted unit to the left.

STEP 11

Finally, make sure that the graph passes through the y-intercept and approaches the horizontal asymptote as described.
The graph of $y=3.^{x+}-$ should now be correctly sketched.

Was this helpful?

QuestionSketch the graph of the function $y=3.2^{x+1}-1$ .

Studdy Solution

STEP 1

Assumptions1. The function is $y=3.^{x+1}-1$ . The function is an exponential function, as it is in the form $y=a^{x}$
3. The base of the exponential function is3.4. The function has been shifted1 unit to the left and1 unit down

STEP 2

First, we need to identify the key features of the graph. These include the y-intercept, the horizontal asymptote, and the general shape of the graph.
The y-intercept is the point where the graph crosses the y-axis. This occurs when $x=0$ . $y =.2^{0+1}-1$

STEP 3

Calculate the y-intercept by plugging in $x=0$ into the function.
$y =3.2^{1}-1$

STEP 4

Calculate the y-intercept.
$y =3.2-1 =2.2$ So the y-intercept is at (0,2.2).

STEP 5

The horizontal asymptote of an exponential function is usually at $y=0$ . However, since our function has been shifted down by1 unit, the horizontal asymptote will be at $y=-1$ .

STEP 6

The general shape of the graph of an exponential function $y=a^{x}$ , where $a>1$ , is that it increases as $x$ increases. Since our base is3.2, which is greater than1, our graph will also have this general shape.

STEP 7

Now, we can start sketching the graph. First, draw the horizontal asymptote at $y=-1$ .

STEP 8

Plot the y-intercept at (0,2.2).

STEP 9

Since the graph increases as $x$ increases, draw the graph so that it is getting closer to the horizontal asymptote as $x$ decreases and getting farther from the horizontal asymptote as $x$ increases.

STEP 10

Remember that the graph has been shifted unit to the left. This means that for any given $x$ , the corresponding $y$ value on our graph will be the $y$ value of $y=3.2^{x}$ shifted unit to the left.

STEP 11

Finally, make sure that the graph passes through the y-intercept and approaches the horizontal asymptote as described.
The graph of $y=3.^{x+}-$ should now be correctly sketched.

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionSketch the graph of the function y=3.2x+1−1y=3.2^{x+1}-1y=3.2x+1−1.

Studdy Solution

STEP 1

Assumptions1. The function is y=3.x+1−1y=3.^{x+1}-1y=3.x+1−1 . The function is an exponential function, as it is in the form y=axy=a^{x}y=ax3. The base of the exponential function is3.4. The function has been shifted1 unit to the left and1 unit down

STEP 2

First, we need to identify the key features of the graph. These include the y-intercept, the horizontal asymptote, and the general shape of the graph.The y-intercept is the point where the graph crosses the y-axis. This occurs when x=0x=0x=0.y=.20+1−1y =.2^{0+1}-1y=.20+1−1

STEP 3

Calculate the y-intercept by plugging in x=0x=0x=0 into the function.y=3.21−1y =3.2^{1}-1y=3.21−1

STEP 4

Calculate the y-intercept.y=3.2−1=2.2y =3.2-1 =2.2y=3.2−1=2.2So the y-intercept is at (0,2.2).

STEP 5

The horizontal asymptote of an exponential function is usually at y=0y=0y=0. However, since our function has been shifted down by1 unit, the horizontal asymptote will be at y=−1y=-1y=−1.

STEP 6

The general shape of the graph of an exponential function y=axy=a^{x}y=ax, where a>1a>1a>1, is that it increases as xxx increases. Since our base is3.2, which is greater than1, our graph will also have this general shape.

STEP 7

Now, we can start sketching the graph. First, draw the horizontal asymptote at y=−1y=-1y=−1.

STEP 8

Plot the y-intercept at (0,2.2).

STEP 9

Since the graph increases as xxx increases, draw the graph so that it is getting closer to the horizontal asymptote as xxx decreases and getting farther from the horizontal asymptote as xxx increases.

STEP 10

Remember that the graph has been shifted unit to the left. This means that for any given xxx, the corresponding yyy value on our graph will be the yyy value of y=3.2xy=3.2^{x}y=3.2x shifted unit to the left.

STEP 11

Finally, make sure that the graph passes through the y-intercept and approaches the horizontal asymptote as described.The graph of y=3.x+−y=3.^{x+}-y=3.x+− should now be correctly sketched.

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionSketch the graph of the function $y=3.2^{x+1}-1$ .

Assumptions1. The function is $y=3.^{x+1}-1$ . The function is an exponential function, as it is in the form $y=a^{x}$
3. The base of the exponential function is3.4. The function has been shifted1 unit to the left and1 unit down

First, we need to identify the key features of the graph. These include the y-intercept, the horizontal asymptote, and the general shape of the graph.
The y-intercept is the point where the graph crosses the y-axis. This occurs when $x=0$ . $y =.2^{0+1}-1$

Calculate the y-intercept by plugging in $x=0$ into the function.
$y =3.2^{1}-1$

Calculate the y-intercept.
$y =3.2-1 =2.2$ So the y-intercept is at (0,2.2).

The horizontal asymptote of an exponential function is usually at $y=0$ . However, since our function has been shifted down by1 unit, the horizontal asymptote will be at $y=-1$ .

The general shape of the graph of an exponential function $y=a^{x}$ , where $a>1$ , is that it increases as $x$ increases. Since our base is3.2, which is greater than1, our graph will also have this general shape.

Now, we can start sketching the graph. First, draw the horizontal asymptote at $y=-1$ .

Since the graph increases as $x$ increases, draw the graph so that it is getting closer to the horizontal asymptote as $x$ decreases and getting farther from the horizontal asymptote as $x$ increases.

Remember that the graph has been shifted unit to the left. This means that for any given $x$ , the corresponding $y$ value on our graph will be the $y$ value of $y=3.2^{x}$ shifted unit to the left.

Finally, make sure that the graph passes through the y-intercept and approaches the horizontal asymptote as described.
The graph of $y=3.^{x+}-$ should now be correctly sketched.