The correct answer is option D. Which is the even function is f (x) = x⁴.
<h3>What is an even function?</h3>
The function in which when the sign of the input variable is changed the output remains the same is called the even function. Mathematically we can write it as f(x) = f(-x ).
let us check the given four options:-
A f(x) = √x ; f(-x) = √-x here f(x) ≠ f(-x)
B f(x) = x ; f(-x) = -x here f(x) ≠ f(-x)
C f(x) = x³ + 1 ; f(-x) = -x³ + 1 here f(x) ≠ f(-x)
D f(x) = x⁴ ; f(-x) = (-x)⁴ = x⁴ here f(x) = f(-x)
We can see that in the option D the f(x) = x⁴ is an even function because f(x) = f(-x).
Therefore the correct answer is option D. Which is the even function is f (x) = x⁴.
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Basically, you have two circles. You are asked to take circle 1 and "move it" so that it is on top of circle 2. This process of moving is called a translation and can be thought of as sliding. You do this by ensuring that the two have the same center. So, starting at (-4,5) how do you have to move to end up at (2,1)?
To do this we need to move right 6 as the x-coordinate goes from -4 to 2. We also need to move down 4 as the y-coordinate goes from 5 to 1. So we add 6 to the x-coordinate and subtract 4 from the y-coordinate. The transformation rule is (x+6, y-4).
Once you do this the circles have the same center. Next you wish to dilate circle 1 so it ends up being the same size at circle 2. That means you stretch it out in such a way that it keeps its shape. Circle 1 has a radius of 2 centimeters and circle 2 has a radius of 6 centimeters. That is 3x bigger. So we dilate by a factor of 3.
Translations and dilations (along with reflections and rotations) belong to a group known as transformations.
-38 > -83
Where Andrew and his father are scuba diving has a higher elevation than tackle box Canyon.
Answer: A 13.4
Step-by-step
a^2 + b^2= c^2 4^2 + b^2 = 14^2 16+ b^2= 195 b^2= 180 b= square root of 180 b= 6 square root of 5 or 13.42
