Question

Describe the following function in terms of basic functions such as unit step function and ramp function.

a) Linear
b) Quadratic
c) Exponential
d) Logarithmic

Answer 1

Linear functions are represented by straight lines, quadratic functions form parabolic curves, exponential functions exhibit exponential growth or decay, and logarithmic functions are the inverses of exponential functions.

Step-by-step explanation:

a) Linear: A linear function represents a straight line. It can be defined as f(x) = mx + b, where m is the slope and b is the y-intercept. An example of a linear function is f(x) = 2x + 3.

b) Quadratic: A quadratic function represents a parabolic curve. It can be defined as f(x) = ax^2 + bx + c, where a, b, and c are constants. An example of a quadratic function is f(x) = x^2 + 2x + 1.

c) Exponential: An exponential function represents exponential growth or decay. It can be defined as f(x) = ab^x, where a and b are constants. An example of an exponential function is f(x) = 2 * 3^x.

d) Logarithmic: A logarithmic function represents the inverse of an exponential function. It can be defined as f(x) = log_b(x), where b is the base. An example of a logarithmic function is f(x) = log_2(x).