Questions: Graph the given functions, (f) and (g), in the same rectangular coordinate system. Describe how the graph of (g) is related to the graph of (f). (f(x)=-x^2) (g(x)=-x^2+2)

Graph the given functions, (f) and (g), in the same rectangular coordinate system. Describe how the graph of (g) is related to the graph of (f).

(f(x)=-x^2)

(g(x)=-x^2+2)

Transcript text: Graph the given functions, $f$ and $g$, in the same rectangular coordinate system. Describe how the graph of $g$ is related to the graph of $f$. \[ \begin{array}{l} f(x)=-x^{2} \\ g(x)=-x^{2}+2 \end{array} \]

Solution

Solution Steps

Step 1: Identify the given functions

The given functions are: \[ f(x) = -x^2 \] \[ g(x) = -x^2 + 2 \]

Step 2: Describe the relationship between the graphs of $ f $ and $ g $

The graph of $ g(x) = -x^2 + 2 $ is a vertical translation of the graph of $ f(x) = -x^2 $ by 2 units upwards.

Final Answer

The graph of $ g(x) = -x^2 + 2 $ is obtained by shifting the graph of $ f(x) = -x^2 $ vertically upwards by 2 units.

{"axisType": 3, "coordSystem": {"xmin": -3, "xmax": 3, "ymin": -3, "ymax": 3}, "commands": ["y = -x2", "y = -x2 + 2"], "latex_expressions": ["$y = -x^2$", "$y = -x^2 + 2$"]}

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