What kind of transformation converts the graph of f(x) = -(x + 5)^2 + 10 into the graph of g(x) = -(x + 5)^2 + 6? Choices: (A)translation 4 units left (B)translation 4 units down (C)translation 4 units up (D)translation 4 units right

Compare Functions: To determine the type of transformation, we need to compare the two functions f(x) and g(x). We will look at the constants at the end of each function to see how they differ.Identify Difference: The original function is f(x) = -(x + 5)^2 + 10. The new function is g(x) = -(x + 5)^2 + 6. The only difference between f(x) and g(x) is the constant term at the end of the equation.Calculate Vertical Shift: The constant term in f(x) is +10, and the constant term in g(x) is +6. To go from +10 to +6, we subtract 4. This means the graph of f(x) has been moved down by 4 units to get the graph of g(x).Determine Transformation: Since the graph has been moved vertically down by 4 units, the correct transformation is a translation 4 units down.

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What kind of transformation converts the graph of $f(x) = -(x + 5)^2 + 10$ into the graph of $g(x) = -(x + 5)^2 + 6$ ? $\newline$ Choices: $\newline$ (A) translation $4$ units left $\newline$ (B) translation $4$ units down $\newline$ (C) translation $4$ units up $\newline$ (D) translation $4$ units right

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Precalculus

Describe function transformations

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Q. What kind of transformation converts the graph of

f(x) = -(x + 5)^2 + 10

into the graph of

g(x) = -(x + 5)^2 + 6

\newline

Choices:

\newline

(A) translation

4

units left

\newline

(B) translation

4

units down

\newline

4

units up

\newline

(D) translation

4

units right

Compare Functions: To determine the type of transformation, we need to compare the two functions $f(x)$ and $g(x)$ . We will look at the constants at the end of each function to see how they differ.
Identify Difference: The original function is $f(x) = -(x + 5)^2 + 10$ . The new function is $g(x) = -(x + 5)^2 + 6$ . The only difference between $f(x)$ and $g(x)$ is the constant term at the end of the equation.
Calculate Vertical Shift: The constant term in $f(x)$ is $+10$ , and the constant term in $g(x)$ is $+6$ . To go from $+10$ to $+6$ , we subtract $4$ . This means the graph of $f(x)$ has been moved down by $4$ units to get the graph of $g(x)$ .
Determine Transformation: Since the graph has been moved vertically down by $4$ units, the correct transformation is a translation $4$ units down.