공부

Exponential Functions Any function of the form \( f(x)=b^x,\ where\ b>0, b\neq 1 \) is an exponential function with base \( b \) and exponent \( x \) . Exponential functions have constant bases and variable exponents. Note that a function of the form \( f(x)=x^b \) for some constant \( b \) is not an exponential function but a power function. ※ Evaluating Exponential Functions If \( x \) is a po..

Existence of an Inverse Function Given a function f and an output y = f(x), we are often interested in finding what value or values x were mapped to y by f. For example, consider the function f(x) = x + 4. Since any output y = x +4, we can solve this equation for x to find that the input is x = y - 4. This equation defines x as a function of y. Denoting this function as f^−1, and writing x = f^-..

Radian Measure Although we can use both radians and degrees, radians are a more natural measurement because they are related directly to the unit circle, a circle with radius 1. Given an angle θ, let s be the length of the corresponding arc on the unit circle. We say the angle corresponding to the arc of length 1 has radian measure 1. Since an angle of 360° corresponds to the circumference of a ..

Linear Functions and Slope Linear functions : functions which have the form f(x) = ax + b, where a and b are constants Slope : the change in y for each unit change in x(this ratio is independent of the points chosen), measurement of both the steepness and the direction of a line We conclude that the formula f(x) = ax + b tells us the slope, a, and the y-intercept, for this line. Sometimes it is ..

Functions Elements : input(independent variable), output(dependent variable), Sets : domain(set of inputs), range(set of outputs) Rule for assigning each input to exactly one output : relation from domain to range ※ Expression of sets with an infinite number of elements 1. Set-builder notation : {x l 1