Which of the following is an even function? (A) g(x)=5x+2 (B) g(x)=x (C) g(x)= x 2 (D) g(x)=x3 (E) g(x)=−|x|

Step-by-step explanation:

If f(x) is an even function, then f(-x) = f(x).

(A)

g(x) = 5x + 2

g(-x) = 5(-x) + 2 = -5x + 2

g(-x) ≠ g(x)

(B)

g(x) = g(x) = x

g(-x) = -x

g(-x) ≠ g(x)

(C)

g(x) = x²

g(-x) = (-x)² = (-1x)² = (-1)²(x)² = x²

g(-x) = g(x)

(D)

g(x) = x³

g(-x) = (-x)³ = (-1x)³ = (-1)³(x)³ = -1x³ = -x³

g(-x) ≠ g(x)

(E)

g(x) = -|x|

g(-x) = -|-x| = -|-1x| = -(|-1|)(|x|) = -1|x| = -|x|

g(-x) = g(x)

175

step-by-step explanation:

2 inches x 10 miles = 200 miles - 3 inches = 175

step-by-step explanation:

f(x)=2x^2 -1 

translation is a function transformation that transform the function in a way of translating. by translating the function its graph is moved  up an down. moving the function f(x) 2 units to the left will be the new function g(x) with the equation: g(x)=f(x+2)=2(x+2)^2 -1