Linear, Quadratic, or Exponential? Graphs & Equations

What is the difference between a linear and a quadratic function?

• A linear function has a constant rate of change, while a quadratic function has a variable rate of change.

• A linear function is represented by a straight line, while a quadratic function is represented by a curve.

• A linear function can have multiple outputs for a single input, while a quadratic function cannot.

• A linear function always intersects the y-axis at one point, while a quadratic function can intersect at two points.

What is the general form of an exponential function?

• f(x) = a + b^x, where a is a constant and b is the base of the exponential.

• f(x) = a * b^x, where a is a constant and b is the base of the exponential.

• f(x) = a - b^x, where a is a constant and b is the base of the exponential.

• f(x) = a / b^x, where a is a constant and b is the base of the exponential.

What is the domain of an exponential function?

• All real numbers.

• Only positive numbers.

• Only negative numbers.

• All integers.

What is the slope of a linear function?

• The slope represents the rate of change of the function and is constant.

• The slope is the y-intercept of the function.

• The slope indicates the maximum value of the function.

• The slope is the distance between two points on the graph.

What is the general form of a quadratic function?

• f(x) = ax^2 + bx + c, where a, b, and c are constants and a ≠ 0.

• f(x) = ax^3 + bx^2 + c, where a, b, and c are constants and a ≠ 0.

• f(x) = a/x^2 + b/x + c, where a, b, and c are constants and a ≠ 0.

• f(x) = ax^2 + b, where a and b are constants and a ≠ 0.

What is the y-intercept of a function?

• The point where the graph intersects the y-axis (x=0).

• The point where the graph intersects the x-axis (y=0).

• The maximum value of the function on the graph.

• The minimum value of the function on the graph.

What is a real-world example of an exponential function?

• Population growth can often be modeled by an exponential function.

• The speed of a car traveling at a constant rate.

• The height of a tree growing at a steady pace.

• The amount of money in a bank account with a fixed interest rate.

What are the three main types of function families in algebra?

• Linear, Quadratic, Exponential

• Polynomial, Logarithmic, Trigonometric

• Rational, Absolute, Piecewise

• Cubic, Quartic, Quintic

What is the general form of a linear function?

• f(x) = mx + b, where m is the slope and b is the y-intercept.

• f(x) = ax^2 + bx + c, where a, b, and c are constants.

• f(x) = m(x - h) + k, where (h, k) is the vertex.

• f(x) = e^x, where e is the base of the natural logarithm.

How can you identify an exponential function from its graph?

• An exponential function's graph shows rapid growth or decay, and is not a straight line.

• An exponential function's graph is always a straight line.

• An exponential function's graph oscillates between two values.

• An exponential function's graph is a circle.