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)

Question

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)

Accepted Answer

∻Solution by Steps∻ ‖ step 1 ⋮ To identify the correct graph for the function $f(x, y) = \sin(y) - x^2$, we need to consider the characteristics of the function. ‖ ‖ 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.◊What is the relationship between the graph of the function $f(x, y) = \sin(y) - x^2$ and the wave-like pattern along the y-axis and the parabolic curvature along the x-axis?⍭ Generate me a similar question◊⚹

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