The function $f: x \mapsto 3\sin(2x)$ is defined for $x \in \mathbb{R}$ - Leaving Cert Mathematics - Question 5 - 2012
Question 5
The function $f: x \mapsto 3\sin(2x)$ is defined for $x \in \mathbb{R}$.
(a) Complete the table below
| x | 0 | \frac{\pi}{4} | \frac{\pi}{2} | \f... show full transcript
Worked Solution & Example Answer:The function $f: x \mapsto 3\sin(2x)$ is defined for $x \in \mathbb{R}$ - Leaving Cert Mathematics - Question 5 - 2012
Step 1
Complete the table below
96%
114 rated
Only available for registered users.
Sign up now to view full answer, or log in if you already have an account!
Answer
x
0
\frac{\pi}{4}
\frac{\pi}{2}
\frac{3\pi}{4}
\pi
2x
0
\frac{\pi}{2}
\pi
\frac{3\pi}{2}
2\pi
\sin(2x)
0
1
0
-1
0
3\sin(2x)
0
3
0
-3
0
Step 2
Draw the graph of $y = f(x)$ in the domain $0 \leq x \leq \pi$, $x \in \mathbb{R}$.
99%
104 rated
Only available for registered users.
Sign up now to view full answer, or log in if you already have an account!
Answer
The graph can be sketched by plotting the points from the completed table and connecting them smoothly to reflect the properties of the sine function, ensuring that the maximum point is at (\frac{\pi}{4}, 3) and the minimum at (\frac{3\pi}{4}, -3).
Step 3
Write down the range and the period of $f$.
96%
101 rated
Only available for registered users.
Sign up now to view full answer, or log in if you already have an account!
Answer
The range of f is given as [-3, 3], meaning the function oscillates between these values. The period of the function is π, which indicates the interval after which the function values repeat.
Join the Leaving Cert students using SimpleStudy...
