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Chapter Two - PreCalculus 2

Chapter Two - PreCalculus 2
Denis Shubleka

If f is a function, then f(s + t) = f(s) + f(t). (1 point)

True
False

If f(s) = f(t), then s = t. (1 point)

True
False

If f is a function, then f(3x) = 3f(x). (1 point)

True
False

If x₁ < x₂ and f is a decreasing function, then
f(x₁) > f(x₂). (1 point)

True
False

A vertical line intersects the graph of a function at most once. (1 point)

True
False

If f and g are functions, then f(g(x)) = g(f(x)). (1 point)

True
False

The average rate of change of a quadratic function is always nonnegative. (1 point)

True
False

The average rate of change of a linear function is equal to its slope. (1 point)

True
False

If the average rate of a function is always zero then the function must be constant. (1 point)

True
False

A function cannot be both even and odd. (1 point)

True
False

The graph of an even function is symmetric with respect to the y-axis. (1 point)

True
False

The graph of an odd function is symmetric with respect to the x-axis. (1 point)

True
False

A function f(x) is even if and only if f(x)=f(-x) for all x values in the domain. (1 point)

True
False

A function is odd if and only f(-x)=-f(x) for all x values in the domain. (1 point)

True
False

If f and g are both even, then f+g is also even. (1 point)

True
False

If f and g are both odd, then f+g is even. (1 point)

True
False

If f is even and g is odd, then f+g is odd. (1 point)

True
False

If f and g are both odd, then fg is always odd. (1 point)

True
False

If f and g are both even, then fg is always even. (1 point)

True
False

If f is even and g is odd, then fg is always odd. (1 point)

True
False

f(x) and g(x) are inverses of each other if and only f(g(x))=g(f(x))=x for all x values in the domain. (1 point)

True
False

The composition of two linear functions is a quadratic function. (1 point)

True
False

All increasing functions are one-to-one. (1 point)

True
False

Some one-to-one functions fail to have inverses. (1 point)

True
False

The Horizontal Line Test on f determines whether the inverse mapping of f is also a function. (1 point)

True
False