Semester 1 Review PreAP - Part 1

Front

Identify intervals on which the function is increasing, decreasing, or constant: f(x) = |x + 2| + |x - 6|

Back

Increasing on (6, ∞); decreasing on (-∞, -2); constant on (−2, 6)

Front

What is the inverse of the function f(x) = 5x - 8?

Back

f^{-1}(x) = \frac{1}{5}x + \frac{8}{5}

Front

Simplify: log x^7 - log x^3 = ?

Back

4 log x

Front

A person flying a kite has released 100 m of string. The string makes an angle of 67° with the ground. How high is the kite?

Back

92.050 ft

Front

Solve for x: x = ?

Back

30.256°

Front

What is the definition of an increasing function?

Back

A function is increasing on an interval if for any two points x1 and x2 in that interval, if x1 < x2, then f(x1) < f(x2).

Front

What is the definition of a decreasing function?

Back

A function is decreasing on an interval if for any two points x1 and x2 in that interval, if x1 < x2, then f(x1) > f(x2).

Front

What is the definition of a constant function?

Back

A function is constant on an interval if for any two points x1 and x2 in that interval, f(x1) = f(x2).

Front

What is the formula for finding the inverse of a linear function?

Back

To find the inverse of f(x) = ax + b, swap x and y and solve for y: y = \frac{x - b}{a}.

Front

What is the logarithmic identity for subtraction?

Back

log_a(b) - log_a(c) = log_a(\frac{b}{c}).