QuestionMary types 65 words/min for 30 min, $T(x)=65x$ . Interpret $P(25)=1625$ and find the domain and range.

Studdy Solution

STEP 1

Assumptions1. Mary can type65 words per minute with no errors for at most half an hour. . The function $(x)=65x$ represents the total number of words Mary can type in $x$ minutes.
3. $(25)=1625$ is a point on the graph of the function $(x)$ .
4. The domain of a function represents all possible input values (in this case, time in minutes).
5. The range of a function represents all possible output values (in this case, the number of words typed).

STEP 2

Interpret the point $(25)=1625$ in the context of the problem.
The point $(25)=1625$ means that when $x=25$ (i.e., after25 minutes), the total number of words that Mary has typed is1625.
$(25)=(25)=65 \times25 =1625$

STEP 3

etermine the domain of the function $(x)$ .
Since Mary can type for at most half an hour (or30 minutes), the domain of the function is all real numbers from0 to30, inclusive.
$Domain0 \leq x \leq30$

STEP 4

etermine the range of the function $(x)$ .
Since Mary types65 words per minute, the minimum number of words she can type is0 (when $x=0$ ) and the maximum is $65 \times30 =1950$ (when $x=30$ ). So the range of the function is all real numbers from0 to1950, inclusive.
$Range0 \leq(x) \leq1950$ In conclusion, the point $(25)=162$ means that Mary has typed162 words after25 minutes. The domain of the function is $0 \leq x \leq30$ and the range is $0 \leq(x) \leq1950$ .

Was this helpful?

Get Studdy

Scan QR code with your device to get Studdy on iOS or Android

QR code

Studdy solves anything!

Download the app

Start learning now

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

Parents Influencer program Contact Policy Terms