Write the equation for an absolute values function translated 3 units to the right and vertically stretched by a factor of 4
translated 3 units to the right
|x-3|
vertically stretched by a factor of 4
4|x-3|
Why did the absolute value function go to the gym? Because it wanted to get vertically stretched by a factor of 4, of course! And it decided to also take a detour and go 3 units to the right. So, the equation for this absolute value function is:
f(x) = 4|X - 3|
The equation for the absolute value function is y = |x|.
To translate the absolute value function 3 units to the right, we can use the equation y = |x - a|, where 'a' is the amount of translation. In this case, a = 3, so the equation becomes y = |x - 3|.
To vertically stretch the function by a factor of 4, we can multiply the entire equation by 4. So, the final equation becomes y = 4|x - 3|.
To write the equation for the absolute value function translated 3 units to the right and vertically stretched by a factor of 4, you would start with the standard absolute value function equation:
f(x) = |x|
To translate the function 3 units to the right, you would replace "x" with "(x - h)" where "h" is the horizontal translation distance. In this case, "h" represents the translation of 3 units to the right. So the translated equation becomes:
f(x) = |(x - 3)|
Next, to vertically stretch the function by a factor of 4, you would multiply the entire expression inside the absolute value brackets by the stretching factor. The stretching factor, in this case, is 4. Therefore, the equation becomes:
f(x) = 4|(x - 3)|
So, the equation for the absolute value function translated 3 units to the right and vertically stretched by a factor of 4 is f(x) = 4|(x - 3)|.