APPC S1 Final Practice - 100 questions!!

Front

What is the property of logarithms that allows you to combine logs with the same base?

Back

The property states that \( \log_b(m) + \log_b(n) = \log_b(m \cdot n) \).

Front

What is the domain of the function \( f(x) = \frac{x}{2x + 4} \)?

Back

The domain is \( (-\infty, -2) \cup (-2, \infty) \) because the function is undefined when the denominator is zero.

Front

How do you find the horizontal asymptote of a rational function?

Back

To find the horizontal asymptote, compare the degrees of the numerator and denominator. If the degree of the numerator is less than the degree of the denominator, the asymptote is \( y = 0 \). If they are equal, the asymptote is \( y = \frac{a}{b} \) where \( a \) and \( b \) are the leading coefficients.

Front

What does it mean to solve an equation using the Least Common Denominator (LCD)?

Back

Using the LCD means multiplying all terms in the equation by the least common denominator to eliminate fractions, making it easier to solve.

Front

What is a vertical compression in transformations of functions?

Back

A vertical compression occurs when the output values of a function are multiplied by a factor less than 1, making the graph 'squish' towards the x-axis.

Front

What is the quadratic formula used for?

Back

The quadratic formula \( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \) is used to find the solutions of a quadratic equation of the form \( ax^2 + bx + c = 0 \).

Front

What is the difference between horizontal and vertical stretches in function transformations?

Back

A horizontal stretch occurs when the input values are multiplied by a factor greater than 1, while a vertical stretch occurs when the output values are multiplied by a factor greater than 1.

Front

What is the significance of the discriminant in a quadratic equation?

Back

The discriminant \( b^2 - 4ac \) determines the nature of the roots: if positive, there are two real roots; if zero, one real root; if negative, two complex roots.

Front

How do you determine the range of a function?

Back

The range of a function is the set of all possible output values. It can be found by analyzing the function's behavior and any restrictions on the output.

Front

What is a logarithmic equation?

Back

A logarithmic equation is an equation that involves a logarithm, such as \( \log_b(x) = y \), which can be rewritten in exponential form as \( b^y = x \).