Domain and Range
What is the domain of the linear function f(x)=2x+3?
all real numbers, or (−∞,∞)(−∞,∞)
Describe the behavior of a linear function's graph as it moves from left to right.
either increasing (if the slope is positive) or decreasing (if the slope is negative) as it moves from left to right
What is the minimum point of the quadratic function f(x)=x2−5
(0,-5)
List three key features of linear functions
Three key features of linear functions include a constant slope, a straight-line graph, and no maximum or minimum points
What starts with T, ends with T, and has T in it?
A teapot
What is the formula for calculating the average rate of change
Average Rate of Change=
(y2 - y1)/(x2 - x1)
How does the range of a quadratic function differ from that of a linear function?
The range of a quadratic function is typically limited depending on if it opens up or down, whereas the range of a linear function is all real numbers.
For the quadratic function f(x)=x2, where does it increase and where does it decrease?
decreases on the interval (−∞,0)(−∞,0) and increases on the interval (0,∞)(0,∞).
Does the linear function h(x)=−3x+2 have a maximum or minimum? Explain why.
does not have a maximum or minimum; it extends infinitely in both directions.
What are the characteristics of the vertex of a quadratic function
The characteristics of the vertex of a quadratic function include its coordinates, which represent the maximum or minimum point, and it is the point where the graph changes direction
When is a door no longer a door?
When its ajar
If the function f(x) = 3^x, what is the average rate of change from x = 1 to x = 3?
Average rate of change = 9
Identify the domain of the exponential function g(x)=3x
all real numbers, or (−∞,∞)(−∞,∞)
How does the graph of an exponential function behave as x increases?
The graph of an exponential function increases as xx increases, reflecting rapid growth
Identify the maximum value of the function g(x)=−2(x−1)2+3
(1,3)
the line that divides quadratic functions in half
Axis of symetry
Which is correct to say, “The yolk of the egg are white?” or “The yolk of the egg is white?”
Neither, the yolks are yellow.
Calculate the average rate of change for: f(x)=x2+2x
Average rate of change = 6
Can the range of a quadratic function be negative? Explain.
Yes, the range of a quadratic function can be negative if it opens downward.
What is the general trend of a linear function compared to a quadratic function as x approaches infinity?
A linear function has a constant rate of change, while a quadratic function's rate of change increases or decreases as x moves away from the vertex
What is a vertex?
The vertex of a quadratic function is the point where the curve changes direction, and it represents either the maximum or minimum value of the function
How can you tell if a function is linear, quadratic, or exponential based on its graph
You can tell if a function is linear (straight line), quadratic (parabola), or exponential (curved line that grows rapidly) based on the shape of its graph
You see a boat filled with people. It has not sunk, but when you look again you don’t see a single person on the boat. Why?
All the people were married, so there are no “single” people.
For the function f(x) = 2x, calculate the average rate of change between x = 0 and x = 2.
Average rate of change is 4
What are the domain and range of the function h(x)=−x2+4
the domain is all real numbers (−∞,∞)(−∞,∞), and the range is (−∞,4](−∞,4].
Explain the intervals in which the function g(x)=2x−3 is increasing.
increasing for all x-values
What is the vertex of the equation:
5(x+2)2 - 7
(-2, -7)
Compare and contrast the growth rates of linear, quadratic, and exponential functions
Linear functions grow at a constant rate, quadratic functions grow at an increasing rate (parabolic growth), and exponential functions grow at an accelerating rate (exponential growth)
What can you put in a bucket to make it weigh less?
A hole
how does average rate of change of an exponential function differs from that of a linear function?
In a linear function, the rate of change remains constant while in an exponential, the rate of change changes as x changes.