Pre-Calculus HN Semester 1 Exam

Front

What is the center and lengths of a and b for the ellipse equation?

Back

The center is (0,0) with lengths a=5 and b=2.

Front

How do you find the composition of two functions f(x) and g(x)?

Back

To find g(f(x)), substitute f(x) into g(x). For example, if f(x)=x^2 and g(x)=2x+3, then g(f(x))=g(x^2)=2x^2+3.

Front

What is the value of h(5) if h(x) is defined by a specific equation?

Back

The value of h(5) is 7.

Front

How do you identify a system of inequalities from a graph?

Back

Look for the shaded regions and boundary lines. For example, if the graph shows x > 2 and y < -4, that is the corresponding system.

Front

How do you evaluate a function of a function, such as f(g(0))?

Back

First, find g(0), then substitute that value into f. For example, if f(x)=3x+10 and g(x)=x-2, then g(0)=-2 and f(-2)=4.

Front

What is the definition of a function?

Back

A function is a relation that assigns exactly one output for each input.

Front

What is the difference between a linear function and a quadratic function?

Back

A linear function has the form f(x)=mx+b, while a quadratic function has the form f(x)=ax^2+bx+c.

Front

What does the vertex of a parabola represent?

Back

The vertex is the highest or lowest point of the parabola, depending on its orientation.

Front

How do you find the x-intercepts of a quadratic function?

Back

Front

What is the standard form of a circle's equation?

Back