Question

Match each function formula with the corresponding transformation of the parent function y = 5-^x Please help ASAP!!

Answer 1

Answer:

We have the parent function given by, $y=5^{-x}$

1. The function is translated 5 units to the left.

So, we get, $y=5^{-x}$ becomes $y=5^{-(x+5)}$

2. The function is translated 5 units to the right.

So, we get, $y=5^{-x}$ becomes $y=5^{-(x-5)}$

3. The function is translated 5 units upwards.

So, we get, $y=5^{-x}$ becomes $y=5^{-x}+5$

4. The function is translated 5 units downwards.

So, we get, $y=5^{-x}$ becomes $y=5^{-x}-5$

5. The function is reflected across x-axis.

So, we get, $y=5^{-x}$ becomes $y=-5^{-x}$

6. The function is reflected across y-axis.

So, we get, $y=5^{-x}$ becomes $y=5^{-x}$.

Answer 2

Answer:

1. Translated left 5 units              $y=5^{-x-5}$

2. Translated right by 5 units    $y=5^{-x+5}$

3. Translated up by 5 units $y=5^{-x}+5$

4. Translated down by 5 units  $y=5^{-x}-5$

5. Reflected across the x-axis  $y=-5^{-x}$

6. Reflected across the y-axis  $y=5^{x}$

Step-by-step explanation:

The given parent function is

$y=5^{-x}$

The transformation of this function is defined as

$y=5^{-(x+a)}+b$

Where, a represents horizontal shift and b represents vertical shift.

If a>0, then graph shifts a units left and if a<0, then graph shifts a units right.

If b>0, then graph shifts b units up and if b<0, then graph shifts b units down.

1. Translated left 5 units

$y=5^{-x-5}$

2. Translated right by 5 units

$y=5^{-x+5}$

3. Translated up by 5 units

$y=5^{-x}+5$

4. Translated down by 5 units

$y=5^{-x}-5$

5. If graph reflected across the x-axis, then the graph passes through (x,-y).

$-y=5^{-x}$

$y=-5^{-x}$

6. If graph reflected across the y-axis, then the graph passes through (-x,y).

$y=5^{-(-x)}$

$y=5^{x}$

Therefore the required matching is

1. Translated left 5 units              $y=5^{-x-5}$

2. Translated right by 5 units    $y=5^{-x+5}$

3. Translated up by 5 units $y=5^{-x}+5$

4. Translated down by 5 units  $y=5^{-x}-5$

5. Reflected across the x-axis  $y=-5^{-x}$

6. Reflected across the y-axis  $y=5^{x}$