Comparing Linear Quadratic Exponential Characteristics

Identify the type of function: f(x) = 3x + 2

• Exponential function

• Quadratic function

• Linear function

• Logarithmic function

What are the key characteristics of an exponential function?

• The key characteristics of an exponential function are that it grows at an increasing rate and never crosses the x-axis.

• The key characteristics of an exponential function are that it shrinks at an increasing rate and never crosses the x-axis.

• The key characteristics of an exponential function are that it grows at a constant rate and never crosses the x-axis.

• The key characteristics of an exponential function are that it grows at a decreasing rate and always crosses the x-axis.

Identify the type of function: h(x) = 2^x

• Quadratic function

• Logarithmic function

• Exponential function

• Linear function

Analyze the rate of change in the function: y(x) = -2x^2 + 4x - 1

• y'(x) = -4x + 4

• y'(x) = -2x^2 + 4x - 1

• y'(x) = -2x^2 - 4x - 1

• y'(x) = -4x - 4

What characteristics do linear, quadratic and exponential functions have in common. (3 min) Select all that apply.

• (possible)

  y-intercept

• (possible)

  x-intercept

• axis of symmetry

• horizontal asymptote

• Vertex

• What characteristics do linear, quadratic and exponential functions have alike and different?

Use complete sentences.

Evaluate responses using AI:

OFF

Select the all statements below that are TRUE.

• C is DECREASING LINEAR

• B is EXPONENTIAL DECAY

• C has CONSTANT RATE OF CHANGE

• A has VARIABLE RATE OF CHANGE

Select all statements that are true regarding the function.

• This graph represents exponential growth

• This graph has a y-interept of 1

• The ROC over [0, 2] is 3/2

• The ROC is constant

Two functions are shown below. For what positive minimum value of x will f(x) exceed g(x)? f(x) = x² - 5x + 6 g(x) = 2x + 8

• x = 3

• x = 5

• x = 7

• x = 8

True or False: All increasing exponential functions eventually exceed all increasing linear functions.

• True

• False