Question

For these problems, identify the simple function and describe the translation to that basic graph.

1. y = |x - 10|

2. y = |x| - 9

3. y = √x + 6

4. y = (x - 3/4)^2

Answer 1

2

Step-by-step explanation:

Answer 2

The simple function and translation for each problem are as follows:

• 1. y = |x - 10| - horizontal shift to the right by 10 units.
• 2. y = |x| - 9 - vertical shift downwards by 9 units.
• 3. y = √x + 6 - vertical shift upwards by 6 units.
• 4. y = (x - 3/4)² - horizontal shift to the right by 3/4 units.

Step-by-step explanation:

1. y = |x - 10|

The simple function in this case is y = |x|. The translation to that basic graph is a horizontal shift to the right by 10 units. This means the graph of y = |x - 10| will look exactly like the graph of y = |x|, but shifted 10 units to the right.

2. y = |x| - 9

The simple function in this case is y = |x|. The translation to that basic graph is a vertical shift downwards by 9 units. This means the graph of y = |x| - 9 will look exactly like the graph of y = |x|, but shifted 9 units downwards.

3. y = √x + 6

The simple function in this case is y = √x. The translation to that basic graph is a vertical shift upwards by 6 units. This means the graph of y = √x + 6 will look exactly like the graph of y = √x, but shifted 6 units upwards.

4. y = (x - 3/4)²

The simple function in this case is y = x². The translation to that basic graph is a horizontal shift to the right by 3/4 units. This means the graph of y = (x - 3/4)² will look exactly like the graph of y = x², but shifted 3/4 units to the right.