CH 1 Skills Review

Front

What is the domain of a function?

Back

The domain of a function is the set of all possible input values (x-values) for which the function is defined.

Front

Determine the domain of the function f(x) = 1/(x-1).

Back

The domain is all real numbers except x = 1, which can be expressed as (-∞, 1) ∪ (1, ∞).

Front

Evaluate f(x) = x^2 - 2x when x = -3.

Back

f(-3) = (-3)^2 - 2(-3) = 9 + 6 = 15.

Front

What does it mean to factor a polynomial?

Back

Factoring a polynomial means expressing it as a product of its factors, which are polynomials of lower degrees.

Front

Factor the polynomial y = 3x^2 - 2x - 5.

Back

y = (3x - 5)(x + 1).

Front

What is an x-intercept?

Back

An x-intercept is a point where the graph of a function crosses the x-axis, meaning the output (y-value) is zero.

Front

Determine the x-intercept of the function y = x^2 + 2x + 1.

Back

The x-intercept is (-1, 0).

Front

What is the range of a function?

Back

The range of a function is the set of all possible output values (y-values) that the function can produce.

Front

Determine the range of the function f(x) = x^2.

Back

The range is [0, ∞) since the output is always non-negative.

Front

What is a quadratic function?

Back

A quadratic function is a polynomial function of degree 2, typically in the form f(x) = ax^2 + bx + c.