The graph is attached.

Step-by-step explanation:

The graphs:

f(x) = x + 1 where x < 0

f(x) = 2 where 0 ≤ x ≤ 1

f(x) = x where x > 1

The graph in the attached figure

Step-by-step explanation:

Let

x-------> the input (independent variable)

y-------> the output (dependent variable)

we know that

The equation that represent the situation is equal to

This is a linear equation

To graph the line find the intercepts

The y-intercept is equal to the point ---> value of y when the value of x is equal to zero

The x-intercept is equal to the point ---> value of x when the value of y is equal to zero

Plot the points

the graph in the attached figure

Step-by-step explanation:

substitue values in the table into the equation.

x = 2, then y = 4(2)-3 =>

y= 5

y = -3, then -3 = 4x-3 =>

x = 0

x = -1, then y = 4(-1) - 3 =>

y = -7

x = 3, then y = 4(3) -3 =>

y = 9

y = 1, then 1 = 4x - 3 =>

x = 4

now plot all of these points and create a line from them

Step-by-step explanation:

Plot the y-intercept, (0, 4).

Placing your pencil point there first, move it 5 units to the right and 4 up, arriving at (5, 4+4), or (5, 8).

From (5, 8), move your pencil point 5 units to the right and 2 units down, ending up at (10, 8-2), or (10, 6).

Connect (0, 4) and (5, 8) with a line segment.

Also connect (5, 8) and (10, 6) with a line segment.

My blue dot is the y-intercept.

My red dot is my x-intercept.

Please look at the graph.

Step-by-step explanation:

I can show you my graph and mark it where the x-intercepts and y-intercepts are.

Let's begin.

We have y=2/3 x+4.

Compare this to the slope-intercept form, y=mx+b where m is the slope and b is the y-intercept.

You should see that m=2/3 and b=4.

This means the slope is 2/3 and the y-intercept is 4.

Don't forget slope means rise/run.

So once we graph 4 (plot a point) on the y-axis, then we will use our slope to get to one more point. The slope here tells us to rise 2 and run 3.

Now sometimes our graph is not accurate when drawing by hand so there is a way without graphing that you can find the x- and y-intercepts.

The x-intercept is when the y-coordinate is 0.

The y-intercept is when the x-coordinate is 0.

So to find the x-intercept, I'm going to set y to 0 and solve for x. Like so,

0=2/3 x +4

Subtract 4 on both sides:

-4=2/3 x

Multiply both sides by the reciprocal of 2/3 which is 3/2:

3/2 (-4)=x

Simplify:

-12/2=x

Simplify:

-6=x

Symmetric Property:

x=-6

So the x-intercept is (-6,0).

I actually already have the y-intercept since my equation is in y=mx+b (slope-intercept form). But if it wasn't you could just set x to 0 and solve for y. Like so:

y=2/3 (0)+4

y=0+4

y=4

The y-intercept is (0,4).

Let's go to our graph now.

f(X) = 10 + 5X

f(X) is the total hours for that week

X is the week number after this plan was put in place

Graphically:

10 is the y-intercept; this is when X=0 which is when

the plan went into effect

5 is the change in the y-value for a change of 1 in the

X-value; this will raise the number of games he can

play by 5 each additional week

After 6 weeks Peter would have 36 total hours of gaming. All you have to do is plug 6 in for x, so you would multiply 6 * 4 = 24 and add 12 which equals 36. The number 12 in the equation equals the number of hours Peter played last week, 4 equals the number of hours Peter's parents let him pay per week, and x equals the number of weeks Peter plays his favorite game. Hope this helps.

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