Math  /  Algebra

QuestionDetermine the value of f(49)f(49) given the periodic function below.

Studdy Solution

STEP 1

What is this asking? Find the value of the function at x=49x = 49 using the repeating pattern of the graph. Watch out! Don't get tricked by the graph's complexity; focus on the period and pattern!

STEP 2

1. Understand the period
2. Find the equivalent position
3. Determine the function value

STEP 3

Alright, let's kick this off by figuring out the **period** of the function.
The period is the length of one complete cycle of the wave.
From the description, we know the wave repeats every **10 units** along the x-axis.
So, the period TT is **10**.

STEP 4

Now, we need to find out where x=49x = 49 falls within one of these cycles.
To do this, we calculate the remainder when 4949 is divided by the period 1010.
This will tell us the equivalent position within the cycle.
49÷10=4 remainder 949 \div 10 = 4 \text{ remainder } 9
So, 4949 is equivalent to 99 within the cycle.

STEP 5

Finally, let's find the value of the function at this equivalent position.
From the graph description, the function peaks at y=6y = 6 and troughs at y=6y = -6.
Since 99 is near the end of the cycle, it corresponds to a trough at y=6y = -6.

STEP 6

The value of the function at f(49)f(49) is 6-6.

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