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

Question

Pergunta

Answer 1

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:

$3f(x)$