Question

Which function describes the graph below? On a coordinate plane, a curve crosses the y-axis at (0, 7), decreases to negative 1, and then increases again to 7. y = 8 cosine (x) + 3 y = 4 cosine (x) + 3 y = 4 sine (x) + 3 y = 8 sine (x) + 3

Answer 1

Given:

The curve crosses y axis at (0,7) i.e. when x = 0, y = 7

and decreases to value of -1 and then again increases to value 7.

Let us examine each given function one by one:

1. $y = 8 cos (x) + 3$

Put x = 0

We know that cos 0 = 1

$y = 8 cos (0) + 3\\\Rightarrow y = 8 \times 1 +3 = 11$

But given that y = 7 when x = 0, so not true.

3. $y = 4 sin (x) + 3$

Putting x = 0, we know sin 0 = 0

$y = 4 sin (0) + 3\\\Rightarrow y = 0 +3 = 3$

But given that y = 7 when x = 0, so not true.

4. $y = 8 sin (x) + 3$

Putting x = 0, we know sin 0 = 0

$y = 8 sin (0) + 3\\\Rightarrow y = 0 +3 = 3$

But given that y = 7 when x = 0, so not true.

Option 2.

$y = 4 cos (x) + 3$

Putting x as 0, We know that cos 0 = 1

$y = 4 cos (0) + 3\\y = 4 \times 1 + 3 = 7$

Putting

$x= \pi\\cos\pi = -1$

$y = 4 cos (\pi) + 3\\\Rightarrow y = 4 \times -1 +3 = -4+3=-1$

Hence, the correct option is $y = 4 cos (x) + 3$.

Please find attached graph for the function.

Answer 2

Answer:

The correct answer is: B

Step-by-step explanation: