MAT 172 Exam Part 1 Review

Front

What is the equation for the graph of y = tan(x)?

Back

The equation for the graph of y = tan(x) is a periodic function that has vertical asymptotes at x = (π/2) + nπ, where n is an integer.

Front

Where is the vertex of the parabola given by the equation y = a(x - h)² + k?

Back

The vertex of the parabola is at the point (h, k).

Front

What does the term 'Amplitude' refer to in the context of sine and cosine graphs?

Back

Amplitude represents half the distance between the maximum and minimum values of the graph.

Front

What is the standard form of the equation for an ellipse centered at (h, k)?

Back

The standard form is (x-h)²/a² + (y-k)²/b² = 1, where a and b are the semi-major and semi-minor axes.

Front

What are the equations of the asymptotes for the hyperbola given by 16x² - 9y² + 144 = 0?

Back

The equations of the asymptotes are y = (4/3)x and y = -(4/3)x.

Front

What is the period of the sine function?

Back

The period of the sine function is 2π.

Front

How do you find the vertex of a quadratic function in standard form?

Back

For a quadratic function in standard form y = ax² + bx + c, the vertex can be found using the formula x = -b/(2a).

Front

What is the difference between 'frequency' and 'period' in trigonometric functions?

Back

Frequency is the number of cycles a function completes in a unit interval, while period is the length of one complete cycle.

Front

What is the general form of a conic section?

Back

The general form of a conic section is Ax² + Bxy + Cy² + Dx + Ey + F = 0.

Front

What is the equation of a circle with center (h, k) and radius r?

Back

The equation of a circle is (x-h)² + (y-k)² = r².