F(x)=|x| has undergone shift right of 1 unit and a shift up 3 units followed by a vertical stretch by a factor of 2
Well, look at Mr. F(x) getting all fancy with his transformations! Let's break it down and put on our comedian hats.
First, F(x) = |x| is like a see-saw, with a sharp turn at x = 0. It's a classic!
Now, let's shift this bad boy to the right by 1 unit. You know, because it wanted a change of scenery. So, F(x) packed its bags and moved to the right. Now, instead of starting at x = 0, it starts at x = 1. What a thrill-seeker!
Next up, a shift up 3 units. F(x) was feeling a little short, so it decided to gain some height. Up, up, and away it went, skyrocketing 3 units higher. Who needs a step-ladder when you can just shift up, right?
But it doesn't stop there! F(x) wanted to impress its friends, so it decided to go for a vertical stretch by a factor of 2. Basically, it stretched its arms and legs out wide, doubling in size. Now, instead of just going up, it's going up twice as fast. Look at F(x) go!
So, after all these transformations, the new and improved F(x) = 2| x - 1 | + 3 is ready to take on the world. It's a real showstopper, combining shifts, lifts, and even a bit of stretching. Bravo, F(x), bravo!
To shift the function f(x) = |x| right by 1 unit, we need to replace x with (x - 1). This shift moves the entire function horizontally to the right.
After the shift, the function becomes f(x) = |x - 1|.
Next, we shift the function f(x) = |x - 1| up by 3 units. To achieve this, we add 3 to the function. This shift moves the entire function vertically upwards.
After the vertical shift, the function becomes f(x) = |x - 1| + 3.
Finally, we need to apply a vertical stretch to the function f(x) = |x - 1| + 3. A vertical stretch by a factor of 2 multiplies the function by 2. This transformation stretches the function vertically.
After the vertical stretch, the final function is f(x) = 2(|x - 1| + 3).
To apply a shift right of 1 unit to the function f(x) = |x|, we replace x with (x - 1), as this shifts the graph of the function to the right by 1 unit.
So, the function after the right shift becomes f(x) = |x - 1|.
Next, to apply a shift up of 3 units to the function, we add 3 to the entire function:
f(x) = |x - 1| + 3.
Finally, to apply a vertical stretch by a factor of 2, we multiply the entire function by 2:
f(x) = 2|x - 1| + 6.
Now, we have successfully applied the shift right of 1 unit, shift up of 3 units, and a vertical stretch by a factor of 2 to the function f(x) = |x|.