Pre-Calculus HN Semester 1 Exam

Front

What is the value of f(-3) if f(x) is represented on a graph where f(-3) = -3?

Back

f(-3) = -3

Front

In the equation (x-3)² + (y-2)² = 16, what is the center of the circle?

Back

The center of the circle is (3, 2).

Front

What is the value of cos(θ) if cos(θ) = 3/5?

Back

cos(θ) = \frac{3}{5}

Front

What is the center of the circle represented by the equation (x + 4)² + (y + 3)² = r²?

Back

The center is (h, k) = (-4, -3).

Front

If p(x) = 3x + 4 and q(x) = 2x², what is p(q(x))?

Back

p(q(x)) = 6x² + 4.

Front

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

Back

The general form is (x - h)² + (y - k)² = r², where (h, k) is the center and r is the radius.

Front

How do you find the center of a circle from its equation?

Back

The center (h, k) can be found from the equation (x - h)² + (y - k)² = r².

Front

What does the term 'function composition' mean?

Back

Function composition is applying one function to the results of another function, denoted as (f ∘ g)(x) = f(g(x)).

Front

What is the value of sin(θ) if cos(θ) = 3/5?

Back

Using the Pythagorean identity, sin(θ) = \sqrt{1 - cos^2(θ)} = \sqrt{1 - (\frac{3}{5})^2} = \frac{4}{5}.

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.