Pergunta

inear Function Transformations :Tutorial Drag the tiles to the correct boxes to complete the pairs. Match each transformation with its description. Tiles 3f(x) f(x+3) f(3x) f(x)+3 Pairs shifts f(x)3 units upward square shifts f(x)3 units left square compresses f(x) by a factor of (1)/(3) toward the y-axis square stretches f(x) by a factor of 3 away from the x-axis square
Solução

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FlaviaMestre · Tutor por 5 anos
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To match each transformation with its description, let's analyze the effects of each transformation on the function f(x) :
1. ** f(x) + 3 **: This transformation shifts the graph of f(x) upward by 3 units.
2. ** f(x+3) **: This transformation shifts the graph of f(x) to the left by 3 units.
3. ** f(3x) **: This transformation compresses the graph of f(x) horizontally by a factor of \frac{1}{3}, which is toward the y-axis.
4. ** 3f(x) **: This transformation stretches the graph of f(x) vertically by a factor of 3, which is away from the x-axis.
Now, let's complete the pairs:
- Shifts f(x) 3 units upward: f(x) + 3
- Shifts f(x) 3 units left: f(x+3)
- Compresses f(x) by a factor of \frac{1}{3} toward the y-axis: f(3x)
- Stretches f(x) by a factor of 3 away from the x-axis: 3f(x)
1. ** f(x) + 3 **: This transformation shifts the graph of f(x) upward by 3 units.
2. ** f(x+3) **: This transformation shifts the graph of f(x) to the left by 3 units.
3. ** f(3x) **: This transformation compresses the graph of f(x) horizontally by a factor of \frac{1}{3}, which is toward the y-axis.
4. ** 3f(x) **: This transformation stretches the graph of f(x) vertically by a factor of 3, which is away from the x-axis.
Now, let's complete the pairs:
- Shifts f(x) 3 units upward: f(x) + 3
- Shifts f(x) 3 units left: f(x+3)
- Compresses f(x) by a factor of \frac{1}{3} toward the y-axis: f(3x)
- Stretches f(x) by a factor of 3 away from the x-axis: 3f(x)
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