Question

Write the equation of the transformed graph.
19.) Translate the graph of y=2^x up 13 units.
20.) Reflect the graph of y=2^x in the x-axis, then translate down 8 units.
21.) Reflect the graph of y=sqrx in the y-axis, then translate down 10 units.
22.) Translate the graph of y=x left 9 units and down 1 unit.
23.) Reflect the graph of y=x^2 in the x-axis and translate 3 units to the right.
24.) Translate the graph of y=x^3 left 5 units and up 1 unit.
25.) Reflect the graph of y=|x| in the x-axis, then translate right 4 units and down 6.

Answer 1

Here are the equations of the transformed graphs for each problem:

19.) To translate the graph of \( y = 2^x \) up 13 units, add 13 to the output:
\[
y = 2^x + 13
\]

20.) To reflect the graph of \( y = 2^x \) in the x-axis, negate the entire function, and then translate down 8 units:
\[
y = -2^x - 8
\]

21.) To reflect the graph of \( y = \sqrt{x} \) in the y-axis, replace \( x \) with \( -x \), and then translate down 10 units:
\[
y = -\sqrt{-x} - 10
\]

22.) To translate the graph of \( y = x \) left 9 units and down 1 unit, change \( x \) to \( x + 9 \) and subtract 1:
\[
y = (x + 9) - 1 = x + 8
\]

23.) To reflect the graph of \( y = x^2 \) in the x-axis, negate the entire function, and then translate 3 units to the right:
\[
y = -(x - 3)^2
\]

24.) To translate the graph of \( y = x^3 \) left 5 units and up 1 unit, replace \( x \) with \( x + 5 \) and add 1:
\[
y = (x + 5)^3 + 1
\]

25.) To reflect the graph of \( y = |x| \) in the x-axis, negate the entire function, then translate right 4 units and down 6:
\[
y = -|x - 4| - 6
\]

These equations represent the transformed graphs based on the descriptions provided.