Math

QuestionFind the domain DD and range RR of the piecewise function g(x)={3x7if x<15if x1g(x) = \begin{cases} -3x - 7 & \text{if } x < -1 \\ -5 & \text{if } x \geq -1 \end{cases}.

Studdy Solution

STEP 1

Assumptions1. The function g(x)g(x) is a piecewise function defined as 3x7-3x -7 when x<1x < -1 and 5-5 when x1x \geq -1. . We need to find the domain () and range (R) of this function.

STEP 2

The domain of a function is the set of all possible input values (x-values) which will produce a valid output. For this piecewise function, we need to consider both pieces separately.

STEP 3

For the first piece of the function, 3x7-3x -7, the function is defined for x<1x < -1. So, the part of the domain corresponding to this piece is (,1)(-\infty, -1).

STEP 4

For the second piece of the function, -, the function is defined for x1x \geq -1. So, the part of the domain corresponding to this piece is [1,+)[-1, +\infty).

STEP 5

Combining both parts, the domain of the entire function is (,+)(-\infty, +\infty).
=(,+) = (-\infty, +\infty)

STEP 6

The range of a function is the set of all possible output values (y-values). Again, we need to consider both pieces of the function separately.

STEP 7

For the first piece of the function, 3x7-3x -7, as xx approaches 1-1 from the left, the y-values approach 2-2.

STEP 8

For the second piece of the function, 5-5, the function is a constant and equal to 5-5 for all x1x \geq -1.

STEP 9

Combining both parts, the range of the entire function is (,2]{5}(-\infty, -2] \cup \{-5\}.
R=(,2]{5}R = (-\infty, -2] \cup \{-5\}So, the domain and range of the function g(x)g(x) are =(,+) = (-\infty, +\infty) and R=(,2]{5}R = (-\infty, -2] \cup \{-5\} respectively.

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