Math / Algebra

Question33-46 - Graphing Piecewise Defined Function of the piecewise defined function.
33. $f(x)=\left\{\begin{array}{ll}0 & \text { if } x<2 \\ 1 & \text { if } x \geq 2\end{array}\right.$
34. $f(x)=\left\{\begin{array}{ll}1 & \text { if } x \leq 1 \\ x+1 & \text { if } x>1\end{array}\right.$
35. $f(x)=\left\{\begin{array}{ll}3 & \text { if } x<2 \\ x-1 & \text { if } x \geq 2\end{array}\right.$
36. $f(x)=\left\{\begin{array}{ll}1-x & \text { if } x<-2 \\ 5 & \text { if } x \geq-2\end{array}\right.$
37. $f(x)=\left\{\begin{array}{ll}x & \text { if } x \leq 0 \\ x+1 & \text { if } x>0\end{array}\right.$
38. $f(x)=\left\{\begin{array}{ll}2 x+3 & \text { if } x<-1 \\ 3-x & \text { if } x \geq-1\end{array}\right.$
39. $f(x)=\left\{\begin{array}{ll}-1 & \text { if } x<-1 \\ 1 & \text { if }-1 \leq x \leq 1 \\ -1 & \text { if } x>1\end{array}\right.$
40. $f(x)=\left\{\begin{array}{ll}-1 & \text { if } x<-1 \\ x & \text { if }-1 \leq x \leq 1 \\ 1 & \text { if } x>1\end{array}\right.$

Studdy Solution

STEP 1

What is this asking? We need to graph some funky functions that have different rules depending on the input $\text{x}$ value! Watch out! Make sure to pay attention to whether the inequalities include the endpoints, that's where those filled and empty circles come in handy!

STEP 2

1. Set up the graph
2. Graph each piece

STEP 3

Let's draw our x and y axes, like a cross, giving us four quadrants to work with. Label them 'x' and 'y' so we don't forget which is which!

STEP 4

Our function is defined in two pieces.
When $x < 2$ , $f(x) = 0$ .
When $x \geq 2$ , $f(x) = 1$ .

STEP 5

For $x < 2$ , our function is just a horizontal line at $y = 0$ .
Since it's less than 2, not less than or equal to, we'll put an open circle at the point $(2, 0)$ .

STEP 6

For $x \geq 2$ , our function is a horizontal line at $y = 1$ .
Since it's greater than or equal to 2, we'll use a filled-in circle at $(2, 1)$ .

STEP 7

This time, when $x \leq 1$ , $f(x) = 1$ .
When $x > 1$ , $f(x) = x + 1$ .

STEP 8

For $x \leq 1$ , we have a horizontal line at $y = 1$ . Filled-in circle at $(1, 1)$ because we have less than or equal to.

STEP 9

For $x > 1$ , we have $f(x) = x + 1$ .
This is a line with a slope of 1 and a y-intercept of 1.
We'll start an open circle at $(1, 2)$ and draw the line going up and to the right.

STEP 10

We'll follow the same process for the rest of the problems. Identify the pieces, graph each piece, and pay close attention to those endpoints!
Remember, open circles for strict inequalities ( $<$ or $>$ ) and filled-in circles for inequalities that include the endpoint ( $\leq$ or $\geq$ ).

STEP 11

We've now graphed all the piecewise functions!
Each graph shows the different pieces of the function, joined together at the specific x-values where the rules change.

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Studdy Solution

STEP 1

What is this asking? We need to graph some funky functions that have different rules depending on the input $\text{x}$ value! Watch out! Make sure to pay attention to whether the inequalities include the endpoints, that's where those filled and empty circles come in handy!

STEP 2

1. Set up the graph
2. Graph each piece

STEP 3

Let's draw our x and y axes, like a cross, giving us four quadrants to work with. Label them 'x' and 'y' so we don't forget which is which!

STEP 4

Our function is defined in two pieces.
When $x < 2$ , $f(x) = 0$ .
When $x \geq 2$ , $f(x) = 1$ .

STEP 5

For $x < 2$ , our function is just a horizontal line at $y = 0$ .
Since it's less than 2, not less than or equal to, we'll put an open circle at the point $(2, 0)$ .

STEP 6

For $x \geq 2$ , our function is a horizontal line at $y = 1$ .
Since it's greater than or equal to 2, we'll use a filled-in circle at $(2, 1)$ .

STEP 7

This time, when $x \leq 1$ , $f(x) = 1$ .
When $x > 1$ , $f(x) = x + 1$ .

STEP 8

For $x \leq 1$ , we have a horizontal line at $y = 1$ . Filled-in circle at $(1, 1)$ because we have less than or equal to.

STEP 9

For $x > 1$ , we have $f(x) = x + 1$ .
This is a line with a slope of 1 and a y-intercept of 1.
We'll start an open circle at $(1, 2)$ and draw the line going up and to the right.

STEP 10

We'll follow the same process for the rest of the problems. Identify the pieces, graph each piece, and pay close attention to those endpoints!
Remember, open circles for strict inequalities ( $<$ or $>$ ) and filled-in circles for inequalities that include the endpoint ( $\leq$ or $\geq$ ).

STEP 11

We've now graphed all the piecewise functions!
Each graph shows the different pieces of the function, joined together at the specific x-values where the rules change.

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Studdy Solution

STEP 1

What is this asking? We need to graph some funky functions that have different rules depending on the input x\text{x}x value! Watch out! Make sure to pay attention to whether the inequalities include the endpoints, that's where those filled and empty circles come in handy!

STEP 2

1. Set up the graph2. Graph each piece

STEP 3

Let's **draw** our x and y axes, like a cross, giving us four quadrants to work with. **Label** them 'x' and 'y' so we don't forget which is which!

STEP 4

Our function is defined in **two pieces**.When x<2x < 2x<2, f(x)=0f(x) = 0f(x)=0.When x≥2x \geq 2x≥2, f(x)=1f(x) = 1f(x)=1.

STEP 5

For x<2x < 2x<2, our function is just a **horizontal line** at y=0y = 0y=0.Since it's *less than* 2, not *less than or equal to*, we'll put an **open circle** at the point (2,0)(2, 0)(2,0).

STEP 6

For x≥2x \geq 2x≥2, our function is a **horizontal line** at y=1y = 1y=1.Since it's *greater than or equal to* 2, we'll use a **filled-in circle** at (2,1)(2, 1)(2,1).

STEP 7

This time, when x≤1x \leq 1x≤1, f(x)=1f(x) = 1f(x)=1.When x>1x > 1x>1, f(x)=x+1f(x) = x + 1f(x)=x+1.

STEP 8

For x≤1x \leq 1x≤1, we have a **horizontal line** at y=1y = 1y=1. **Filled-in circle** at (1,1)(1, 1)(1,1) because we have *less than or equal to*.

STEP 9

For x>1x > 1x>1, we have f(x)=x+1f(x) = x + 1f(x)=x+1.This is a **line** with a **slope** of 1 and a y-intercept of 1.We'll start an **open circle** at (1,2)(1, 2)(1,2) and draw the line going up and to the right.

STEP 10

STEP 11

We've now graphed all the piecewise functions!Each graph shows the different pieces of the function, joined together at the specific x-values where the rules change.

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.

What is this asking? We need to graph some funky functions that have different rules depending on the input $\text{x}$ value! Watch out! Make sure to pay attention to whether the inequalities include the endpoints, that's where those filled and empty circles come in handy!

1. Set up the graph
2. Graph each piece

Let's draw our x and y axes, like a cross, giving us four quadrants to work with. Label them 'x' and 'y' so we don't forget which is which!

Our function is defined in two pieces.
When $x < 2$ , $f(x) = 0$ .
When $x \geq 2$ , $f(x) = 1$ .

For $x < 2$ , our function is just a horizontal line at $y = 0$ .
Since it's less than 2, not less than or equal to, we'll put an open circle at the point $(2, 0)$ .

For $x \geq 2$ , our function is a horizontal line at $y = 1$ .
Since it's greater than or equal to 2, we'll use a filled-in circle at $(2, 1)$ .

This time, when $x \leq 1$ , $f(x) = 1$ .
When $x > 1$ , $f(x) = x + 1$ .

For $x \leq 1$ , we have a horizontal line at $y = 1$ . Filled-in circle at $(1, 1)$ because we have less than or equal to.

For $x > 1$ , we have $f(x) = x + 1$ .
This is a line with a slope of 1 and a y-intercept of 1.
We'll start an open circle at $(1, 2)$ and draw the line going up and to the right.

We've now graphed all the piecewise functions!
Each graph shows the different pieces of the function, joined together at the specific x-values where the rules change.