Question

Given the following linear function sketch the graph of the function and find the domain and range. ƒ(x) = -3x + 7

Answer 1

Find the y-intercept (7 because it's in slope-intercept form). That would be (0,7). Plot that point.

Find another point. For example, plug in 1 for x. Then solve for f(x) which would be -3(1) + 7 = 4. That would be (1, 4). Plot that point.

Connect the dots and you have a line.

The domain is (-infinity, infinity) because it's an infinite line.
The range is the same because it's an infinite line.

Answer 2

`\text{Domain: }(-\infty,\infty)`

`\text{Range: }(-\infty,\infty)`

Graph : Attachment

Explanation:

Given:
`f(x)=-3x+7`

We need to graph it and find the domain and range of the function.

Domain: It is input value of x where function is well defined.

`\text{Domain: }(-\infty,\infty)`

Range: It is output value of f(x)

`\text{Range: }(-\infty,\infty)`

Now we draw the graph of f(x) using table method.

So, first we have to make the table of x and y

Put x=-1 into f(x)

f(-1)=-3(-1)+7 = 3+7 = 10

(-1,10)

Put x=1 into f(x)

f(1)=-3(1)+7 = -3+7 = 4

(1,4)

Put x=0 into f(x)

f(0)=-3(0)+7 = 0+7 =7

(0,7)

x : -1 0 1

f(x) : 10 7 4

Now we plot the points on graph. Please find the attachment for graph.