Linear vs Exponential

What is the general form of a linear function?

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

• y = ax^2 + bx + c, where a, b, and c are constants.

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

• y = mx^3 + b, where m is the coefficient of the cubic term.

How does the graph of a linear function look?

• A curved line

• A straight line

• A series of points

• A zigzag line

What is the rate of change for an exponential function?

• The rate of change is constant regardless of the value of the function.

• The rate of change is zero at all points.

• The rate of change for an exponential function is not constant; it increases or decreases based on the current value of the function.

• The rate of change decreases as the function value increases.

How can you identify an exponential function from a table of values?

• An exponential function can be identified by a pattern where the ratio of consecutive y-values is constant.

• An exponential function can be identified by a pattern where the difference between consecutive y-values is constant.

• An exponential function can be identified by a pattern where the y-values increase by a fixed amount.

• An exponential function can be identified by a pattern where the x-values are all the same.

What is the significance of the base in an exponential function?

• The base determines the rate of growth or decay; a base greater than 1 indicates growth, while a base between 0 and 1 indicates decay.

• The base is irrelevant in determining the function's behavior.

• The base only affects the horizontal shift of the graph.

• The base must always be a whole number for the function to be valid.

What does it mean for a function to have a constant rate of change?

• A constant rate of change means that for every unit increase in x, the value of y increases or decreases by a fixed amount.

• A constant rate of change means that the function's output does not change regardless of the input.

• A constant rate of change indicates that the function is quadratic in nature.

• A constant rate of change means that the function's graph is a curve rather than a straight line.

What is the rate of change for a linear function?

• It varies and is represented by the intercept (b) in the equation y = mx + b.

• It is constant and is represented by the slope (m) in the equation y = mx + b.

• It is determined by the y-intercept of the function.

• It changes depending on the value of x.

What is the difference between linear and exponential functions?

• Linear functions have a constant rate of change, while exponential functions have a variable rate of change that increases or decreases multiplicatively.

• Linear functions increase at a decreasing rate, while exponential functions increase at a constant rate.

• Linear functions can only be represented by straight lines, while exponential functions can be represented by curves.

• Linear functions are always positive, while exponential functions can be negative.

How does the graph of an exponential function look?

• The graph is a straight line that remains constant.

• The graph is a curve that increases or decreases rapidly.

• The graph is a series of peaks and valleys.

• The graph is a circle that oscillates between two points.

What is the impact of a negative exponent in an exponential function?

• A negative exponent indicates a growth process, where the function increases as x increases.

• A negative exponent indicates a decay process, where the function approaches zero as x increases.

• A negative exponent has no effect on the function's behavior.

• A negative exponent results in a constant function, regardless of x.