Using Function Notation and Graphing Technology

4.5.4 Using Function Notation and Graphing Technology

4.5.4 • Using Function Notation and Graphing Technology

Activity

The function $B$ is defined by the equation $B (x) = 10 x + 25$ . Use the graphing tool here or technology outside the course. Graph the function.

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If needed, remember -

You can collapse the equation entry tab by selecting the button.
To change the scale along either the x- or $y$ -axis, click on the wrench button and then enter minimum and maximum values for each axis and set the step value.
To find a point on the line, click on the line and drag the mouse along the line to display the ordered pairs for each location.

1. What is the value of $B (6)$ ?

Compare your answer:

$B (6) = 85$

2. What were the window values you used for the $x$ -axis? (Write the values as an inequality.)

Compare your answer:

$- 1 \leq x \leq 7$

3. What were the window values you used for the $y$ -axis? (Write the values as an inequality.)

Compare your answer:

$- 1 \leq y \leq 100$

4. What is the value of $B (2.75)$ ?

Compare your answer:

$B (2.75) = 52.5$

5. What is the value of $B (1.482)$ ?

Compare your answer:

$B (1.482) = 39.8$

6. What is the value of $x$ if $B (x) = 93$ ?

Compare your answer:

$x = 6.8$

7. What were the window values you used for the $x$ -axis? (Write the values as an inequality.)

Compare your answer:

$- 2 \leq x \leq 16$

8. What were the window values you used for the $y$ -axis? (Write the values as an inequality.)

Compare your answer:

$- 15 \leq y \leq 150$

9. What is the value of $x$ if $B (x) = 42.1$ ?

Compare your answer:

$x = 1.71$

10 What is the value of $x$ if $B (x) = 116.25$ ?

Compare your answer:

$x = 9.125$

Self Check

The function $D$ is defined by the equation $D(x)=2.5x +12$ .

Which describes the window that can be used to find the value of $x$ when $D(x)=23.25$ using graphing technology and gives the correct value of $x$ ?

Graph $y=2.5x+12$ , $y=23.25$ ; window: $x$ from 20 to 25, $y$ from 0 to 10; $x=4.5$
Graph $y=2.5x$ , $y=23.25$ ; window: $x$ from 0 to 10, $y$ from 20 to 25; $x=9.3$
Graph $y=2.5x+12$ , $y=23.25$ ; window: $x$ from 0 to 10, $y$ from 20 to 25; $x=4.5$
Graph $y=2.5x+12$ , $x=23.25$ ; window: $x$ from 0 to 30, $y$ from 0 to 100; $x=70.125$

Additional Resources

Finding Missing Values

Function $G$ is defined by $G (x) = 5 x + 20$ . Find the following values using graphing technology.

a. $G (2)$

To find $G (2)$ , look at $x = 2$ on the $x$ -axis on the graph of $G (x)$ . Use proper steps with your graphing technology to find the $y$ -value on the line: $G (2) = 30$ .

Graph of a straight line with y-intercepts of 20 that passes through the point (2, 30).

b. $G (x) = 32$

To find the value of $x$ where $G (x) = 32$ , look at where the graph crosses the $y$ -value of 32. Use proper steps with your graphing technology to find the $x$ -value where the graph meets $y = 32$ .

Graph of a straight line with y-intercepts of 20 that passes through the point (2.4, 32) a green horizontal line that passes through (0, 32).

$G (2.4) = 32$

Try it

Finding Missing Values

Function $H$ is defined by $H (x) = 2 x + 4$ . Find $H (x) = 10.4$ using graphing technology.

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Use the graphing tool here or technology outside the course.

Here is how to find the value of $H (x)$ using graphing technology:To find the value of $x$ where $H (x) = 10.4$ , look at where the graph of $H (x) = 2 x + 4$ crosses the $y$ -value of 10.4. Use proper steps with your graphing technology to find the $x$ -value where the graph meets $y = 10.4$ .

$H (3.2) = 10.4$

Graph of a straight line with y-intercepts of 4 that passes through the point (3.2, 10.4) a red horizontal line that passes through (0, 10.4)