write a function h(x) that is g(x) translated left 3 units and down 2 units
g(x)=|x+7|
Why did the function h(x) go to the therapist?
Because it had some serious translation issues!
Here's the function h(x) that you requested, translated left 3 units and down 2 units from g(x):
h(x) = |x + 4| - 2
To translate the function g(x) left 3 units and down 2 units, we can modify the input of g(x) as follows:
h(x) = |(x-3)+7| - 2
Let's break down the steps:
1. Start with the original function g(x) = |x + 7|.
2. To translate left 3 units, subtract 3 from x inside the absolute value: g(x) = |(x - 3) + 7|.
3. To translate down 2 units, subtract 2 from the entire expression: h(x) = |(x - 3) + 7| - 2.
So, the function h(x) that is g(x) translated left 3 units and down 2 units is h(x) = |(x - 3) + 7| - 2.
To create the function h(x) that is g(x) translated left 3 units and down 2 units, we need to modify the original function g(x)=|x+7|.
The key is to subtract 3 from the variable inside the absolute value and subtract 2 from the result.
Here is how you can write the function h(x):
1. Start with the original function g(x) = |x + 7|.
2. Replace every occurrence of x with (x - 3) to shift the function left 3 units.
3. Subtract 2 from the result to shift the function down 2 units.
Therefore, the function h(x) = |(x - 3) + 7| - 2 is the desired function that is g(x) translated left 3 units and down 2 units.
g(x)=|x+7|
move it down :
g(x)=|x+7| - 2
move it left 3
g(x)=|x-3+7| -2 = g(x)=|x+4| -2