MATH 103 Final Exam Review

Front

What is the solution to the inequality 9x - 5 > 7?

Back

x > \frac{4}{3}

Front

What is the solution set for the inequality x^2 - 3x < 2?

Back

[0,1] ∪ (2,∞)

Front

How do you rationalize the denominator of \sqrt[]{\frac{81}{5}}?

Back

\frac{9\sqrt[]{5}}{5}

Front

What is the formula to find the slope of a line given two points (x1, y1) and (x2, y2)?

Back

Slope = \frac{y2 - y1}{x2 - x1}

Front

How do you find the slope of the line containing the points (-3,-5) and (-7,7)?

Back

The slope is -3.

Front

What transformations are applied to the graph of y = x² to obtain the graph of f(x) = - (x - 7)² + 9?

Back

Shift it horizontally 7 units to the right, reflect it across the x-axis, and shift it 9 units up.

Front

What is the definition of a rational number?

Back

A rational number is any number that can be expressed as the quotient or fraction of two integers.

Front

What is the difference between an open interval and a closed interval?

Back

An open interval (a, b) does not include the endpoints a and b, while a closed interval [a, b] includes both endpoints.

Front

What is the vertex form of a quadratic function?

Back

The vertex form is f(x) = a(x - h)² + k, where (h, k) is the vertex of the parabola.

Front

How do you convert a quadratic function from standard form to vertex form?

Back

You can complete the square to convert from standard form ax² + bx + c to vertex form.