Question

Math

Posted 3 months ago

```
Which graph is generated by the function $f(x, y)=\sin (y)-x^{2} ?$ The positive side of each axis is labeled.
Choose 1 answer:
(A)
(B)
(C)
(D)
```

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Answer from Sia

Posted 3 months ago

Solution by Steps

step 2

The term $\sin(y)$ indicates that there will be a wave-like pattern along the y-axis

step 3

The term $-x^2$ indicates that there will be a parabolic curvature opening downwards along the x-axis

step 4

The correct graph should show both of these features: a wave pattern along the y-axis and a downward parabola along the x-axis

C

Key Concept

Graphical representation of functions

Explanation

The graph of $f(x, y) = \sin(y) - x^2$ should exhibit a sinusoidal pattern along the y-axis due to the $\sin(y)$ term and a parabolic shape along the x-axis due to the $-x^2$ term. The correct graph will combine these two features.

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