Question

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Answer 1

An function is considered to be an even function only if f(-x) = f(x)
1. f(x) = (x-1)^2 = x^2 - 2x + 1
f(-x) = (-x-1)^2 = x^2 + 2x + 1
These two don't match, not an even function

2. f(x) = 8x
f(-x) = -8x
These two don't match, not an even function

3. f(x) = x^2 - x
f(-x) = (-x)^2 - (-x) = x^2 + x
These two don't match, not an even function

4. f(x) = 7
f(-x) = 7
Match, is an even function

Answer 2

An even function is symmetric with respect to the y-axis. One way to identify an even function is to check the exponents of its terms, all of which must be even. For constants, we assume the exponent is zero (still considered an even number for this purpose). The first function will have an odd exponent because the expansion has a 2x term. The second function has 8x, which is also an odd exponent of 1. The third function has an odd exponent in x.
The fourth function is just a constant (with exponent 0), so it is an even function.