What kind of transformation converts the graph of f(x) = 9|x + 10| + 5 into the graph of g(x) = 9|x + 6| + 5? Choices: (A)translation 4 units up (B)translation 4 units down (C)translation 4 units left (D)translation 4 units right

Analyze Functions: Analyze the given functions to determine the type of transformation. The given functions are f(x) = 9|x + 10| + 5 and g(x) = 9|x + 6| + 5. Both functions have the same coefficient for the absolute value expression (9) and the same constant term (+5). The difference lies in the expressions inside the absolute value: |x + 10| for f(x) and |x + 6| for g(x). This suggests a horizontal shift.Determine Shift Direction: Determine the direction of the horizontal shift. The expression inside the absolute value for f(x) is x + 10, and for g(x) it is x + 6. To go from x + 10 to x + 6, we need to subtract 4 from the x-value. This means the graph of f(x) is shifted 4 units to the left to obtain the graph of g(x).Verify with Example: Verify the transformation with an example point. Let's take the point where x = -10 for f(x). Plugging it into f(x), we get f(-10) = 9|(-10) + 10| + 5 = 9|0| + 5 = 5. Now, if we shift this point 4 units to the left, x becomes -10 - 4 = -14. Plugging x = -14 into g(x), we get g(-14) = 9|(-14) + 6| + 5 = 9|-8| + 5 = 9*8 + 5 = 72 + 5 = 77. Since this does not match the y-value of the point on f(x), we have made a mistake in our reasoning.

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What kind of transformation converts the graph of $f(x) = 9|x + 10| + 5$ into the graph of $g(x) = 9|x + 6| + 5$ ? $\newline$ Choices: $\newline$ (A) translation $4$ units up $\newline$ (B) translation $4$ units down $\newline$ (C) translation $4$ units left $\newline$ (D) translation $4$ units right

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Algebra 1

Describe function transformations

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Q. What kind of transformation converts the graph of

f(x) = 9|x + 10| + 5

into the graph of

g(x) = 9|x + 6| + 5

\newline

Choices:

\newline

(A) translation

4

units up

\newline

(B) translation

4

units down

\newline

4

units left

\newline

(D) translation

4

units right

Analyze Functions: Analyze the given functions to determine the type of transformation. The given functions are $f(x) = 9|x + 10| + 5$ and $g(x) = 9|x + 6| + 5$ . Both functions have the same coefficient for the absolute value expression ( $9$ ) and the same constant term ( $+5$ ). The difference lies in the expressions inside the absolute value: $|x + 10|$ for $f(x)$ and $|x + 6|$ for $g(x)$ . This suggests a horizontal shift.
Determine Shift Direction: Determine the direction of the horizontal shift. The expression inside the absolute value for $f(x)$ is $x + 10$ , and for $g(x)$ it is $x + 6$ . To go from $x + 10$ to $x + 6$ , we need to subtract $4$ from the $x$ -value. This means the graph of $f(x)$ is shifted $4$ units to the left to obtain the graph of $g(x)$ .
Verify with Example: Verify the transformation with an example point. $\newline$ Let's take the point where $x = -10$ for $f(x)$ . Plugging it into $f(x)$ , we get $f(-10) = 9|(-10) + 10| + 5 = 9|0| + 5 = 5$ . Now, if we shift this point $4$ units to the left, $x$ becomes $-10 - 4 = -14$ . Plugging $x = -14$ into $g(x)$ , we get $g(-14) = 9|(-14) + 6| + 5 = 9|-8| + 5 = 9\times8 + 5 = 72 + 5 = 77$ . Since this does not match the $f(x)$ $0$ -value of the point on $f(x)$ , we have made a mistake in our reasoning.