Math

QuestionGraph the piecewise function f(x)={x if x32x+1 if x>3f(x)=\left\{\begin{array}{r}x \text { if } x \leq-3 \\ -2 x+1 \text { if } x>-3\end{array}\right. and find its domain DD and range RR.

Studdy Solution

STEP 1

Assumptions1. The function is defined piecewise, meaning it has different definitions for different intervals of x. . The first piece of the function is f(x)=xf(x) = x for x3x \leq -3.
3. The second piece of the function is f(x)=x+1f(x) = -x +1 for x>3x > -3.

STEP 2

We will first graph the piece f(x)=xf(x) = x for xx \leq -. This is a straight line with a slope of1 and y-intercept of0, but we only graph it for xx \leq -.

STEP 3

Next, we graph the piece f(x)=2x+1f(x) = -2x +1 for x>3x > -3. This is a straight line with a slope of -2 and y-intercept of1, but we only graph it for x>3x > -3.

STEP 4

Now that we have graphed both pieces, we can identify the domain and range of the function.

STEP 5

The domain of a function is the set of all possible x-values. For this function, there are no restrictions on x, so the domain is all real numbers, or =(,) = (-\infty, \infty).

STEP 6

The range of a function is the set of all possible y-values. For the first piece of the function, f(x)=xf(x) = x for x3x \leq -3, the y-values are also less than or equal to -3. For the second piece of the function, f(x)=2x+1f(x) = -2x +1 for x>3x > -3, the y-values are greater than -5. So the range is R=(,5)[3,)R = (-\infty, -5) \cup [-3, \infty).

Was this helpful?

Studdy solves anything!

banner

Start learning now

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

ParentsInfluencer programContactPolicyTerms
TwitterInstagramFacebookTikTokDiscord