Alg 2 Sem 1 Final Review

Front

What is the effect of a vertical compression by a factor of \( \frac{1}{2} \) on the function \( f(x) = \sqrt{x} \)?

Back

The function becomes \( f(x) = \frac{1}{2}\sqrt{x} \).

Front

How do you reflect a function in the x-axis?

Back

To reflect a function in the x-axis, multiply the entire function by -1.

Front

What is the transformation for translating a function 3 units left?

Back

Replace \( x \) with \( x + 3 \) in the function.

Front

What is the transformation for translating a function 5 units up?

Back

Add 5 to the entire function.

Front

What is the vertex of the function \( g(x) = 2(x-4)^2 + 8 \)?

Back

The vertex is \( (4, 8) \).

Front

How do you determine if a point is a solution to a nonlinear system?

Back

Substitute the point into each equation of the system; if it satisfies all equations, it is a solution.

Front

What is the vertex of the function \( y = 2|x-3| + 1 \)?

Back

The vertex is \( (3, 1) \).

Front

How do you simplify \( \sqrt{-24} \)?

Back

\( \sqrt{-24} = 2i\sqrt{6} \).

Front

What is the general form of a quadratic function?

Back

The general form is \( f(x) = ax^2 + bx + c \).

Front

What does the vertex of a parabola represent?

Back

The vertex represents the maximum or minimum point of the parabola.