QuestionIdentify the type of transformation for each function: (a) $f(x)=(x+88)^{2}$ , (b) $f(x)=x^{2}+88$ , (c) $f(x)=88 \sqrt{x}$ , (d) $f(x)=\sqrt{88 x}$ .

Studdy Solution

STEP 1

Assumptions1. The graph of $f(x)=x^{}$ is a parabola opening upwards with vertex at the origin. . The graph of $f(x)=\sqrt{x}$ is a curve starting from the origin and increasing as x increases.
3. Shifting a graph left or right involves changing the x-coordinate of each point.
4. Shifting a graph up or down involves changing the y-coordinate of each point.
5. Stretching a graph involves increasing the distance of each point from the origin.
6. Shrinking a graph involves decreasing the distance of each point from the origin.

STEP 2

For (a), the graph of $f(x)=(x+88)^{2}$ can be obtained from shifting the graph of $f(x)=x^{2}$ .
The change is in the x-coordinate, so the shift is horizontal. The sign of the number inside the parentheses is positive, so the shift is to the left.

STEP 3

For (b), the graph of $f(x)=x^{2}+88$ can be obtained from shifting the graph of $f(x)=x^{2}$ .
The change is in the y-coordinate, so the shift is vertical. The number added to the function is positive, so the shift is upward.

STEP 4

For (c), the graph of $f(x)=88 \sqrt{x}$ can be obtained from the graph of $f(x)=\sqrt{x}$ .
The change is a multiplication factor on the y-coordinate, so the change is vertical. The factor is greater than1, so the change is a stretching.

STEP 5

For (d), the graph of $f(x)=\sqrt{88 x}$ can be obtained from the graph of $f(x)=\sqrt{x}$ .
The change is inside the square root, affecting the x-coordinate, so the change is horizontal. The factor inside the square root is greater than1, so the change is a shrinking.

STEP 6

So, the answers are(a) left(b) upward(c) stretching(d) shrinking

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QuestionIdentify the type of transformation for each function: (a) $f(x)=(x+88)^{2}$ , (b) $f(x)=x^{2}+88$ , (c) $f(x)=88 \sqrt{x}$ , (d) $f(x)=\sqrt{88 x}$ .

Studdy Solution

STEP 1

STEP 2

For (a), the graph of $f(x)=(x+88)^{2}$ can be obtained from shifting the graph of $f(x)=x^{2}$ .
The change is in the x-coordinate, so the shift is horizontal. The sign of the number inside the parentheses is positive, so the shift is to the left.

STEP 3

For (b), the graph of $f(x)=x^{2}+88$ can be obtained from shifting the graph of $f(x)=x^{2}$ .
The change is in the y-coordinate, so the shift is vertical. The number added to the function is positive, so the shift is upward.

STEP 4

For (c), the graph of $f(x)=88 \sqrt{x}$ can be obtained from the graph of $f(x)=\sqrt{x}$ .
The change is a multiplication factor on the y-coordinate, so the change is vertical. The factor is greater than1, so the change is a stretching.

STEP 5

For (d), the graph of $f(x)=\sqrt{88 x}$ can be obtained from the graph of $f(x)=\sqrt{x}$ .
The change is inside the square root, affecting the x-coordinate, so the change is horizontal. The factor inside the square root is greater than1, so the change is a shrinking.

STEP 6

So, the answers are(a) left(b) upward(c) stretching(d) shrinking

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QuestionIdentify the type of transformation for each function: (a) f(x)=(x+88)2f(x)=(x+88)^{2}f(x)=(x+88)2, (b) f(x)=x2+88f(x)=x^{2}+88f(x)=x2+88, (c) f(x)=88xf(x)=88 \sqrt{x}f(x)=88x​, (d) f(x)=88xf(x)=\sqrt{88 x}f(x)=88x​.

Studdy Solution

STEP 1

STEP 2

For (a), the graph of f(x)=(x+88)2f(x)=(x+88)^{2}f(x)=(x+88)2 can be obtained from shifting the graph of f(x)=x2f(x)=x^{2}f(x)=x2.The change is in the x-coordinate, so the shift is horizontal. The sign of the number inside the parentheses is positive, so the shift is to the left.

STEP 3

For (b), the graph of f(x)=x2+88f(x)=x^{2}+88f(x)=x2+88 can be obtained from shifting the graph of f(x)=x2f(x)=x^{2}f(x)=x2.The change is in the y-coordinate, so the shift is vertical. The number added to the function is positive, so the shift is upward.

STEP 4

For (c), the graph of f(x)=88xf(x)=88 \sqrt{x}f(x)=88x​ can be obtained from the graph of f(x)=xf(x)=\sqrt{x}f(x)=x​.The change is a multiplication factor on the y-coordinate, so the change is vertical. The factor is greater than1, so the change is a stretching.

STEP 5

For (d), the graph of f(x)=88xf(x)=\sqrt{88 x}f(x)=88x​ can be obtained from the graph of f(x)=xf(x)=\sqrt{x}f(x)=x​.The change is inside the square root, affecting the x-coordinate, so the change is horizontal. The factor inside the square root is greater than1, so the change is a shrinking.

STEP 6

So, the answers are(a) left(b) upward(c) stretching(d) shrinking

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QuestionIdentify the type of transformation for each function: (a) $f(x)=(x+88)^{2}$ , (b) $f(x)=x^{2}+88$ , (c) $f(x)=88 \sqrt{x}$ , (d) $f(x)=\sqrt{88 x}$ .

For (a), the graph of $f(x)=(x+88)^{2}$ can be obtained from shifting the graph of $f(x)=x^{2}$ .
The change is in the x-coordinate, so the shift is horizontal. The sign of the number inside the parentheses is positive, so the shift is to the left.

For (b), the graph of $f(x)=x^{2}+88$ can be obtained from shifting the graph of $f(x)=x^{2}$ .
The change is in the y-coordinate, so the shift is vertical. The number added to the function is positive, so the shift is upward.

For (c), the graph of $f(x)=88 \sqrt{x}$ can be obtained from the graph of $f(x)=\sqrt{x}$ .
The change is a multiplication factor on the y-coordinate, so the change is vertical. The factor is greater than1, so the change is a stretching.

For (d), the graph of $f(x)=\sqrt{88 x}$ can be obtained from the graph of $f(x)=\sqrt{x}$ .
The change is inside the square root, affecting the x-coordinate, so the change is horizontal. The factor inside the square root is greater than1, so the change is a shrinking.