Graphical Features of Functions Assessment

Graphical Features of Functions Assessment

Multiple Choice

What is/are the x-intercept(s)?

• (-1, 0) only

• (0, -1) only

• (1, 0) only

• both (-1, 0) and (1, 0)

Open Ended

What is an x-intercept?

Open Ended

Why can a function have more than one x-intercept?

Open Ended

Why are the x-intercepts called the zeroes of the function?

1. x-intercepts are the points where a function intersects the x-axis.

2. A function can have multiple x-intercepts because multiple input (x) values can have the same output value (y) in a function.

3. x-intercepts are called the zeroes of a function because all the y-coordinates are 0. Recall the value of the function is the value of y.

Multiple Choice

What is/are the y-intercept(s)?

• (-1, 0) only

• (0, -1) only

• (1, 0) only

• both (-1, 0) and (1, 0)

Open Ended

What is the y-intercept?

Open Ended

Why can't a function have more than one y-intercept?

1. The y-intercept is the point where the function intersects the y-axis.

2. A function can't have more than one y-intercept because, if it did, the input (x) value of 0 would have multiple output values. This contradicts the definition of function.

Multiple Choice

On what interval(s) is the function increasing?

• -1 < x < 3

• x < -1 and x > 3

• x < 0 and x > 2

• 0 < x < 2

Open Ended

How can you tell where the graph of a function is increasing?

Open Ended

When identifying intervals where a function is increasing, why do we identify the x values?

1. A function is increasing where its graph slopes upward from left to right.

2. Think cause and effect. We want to know which input values (x values) CAUSE the function (y values) to increase (which is the EFFECT). In this example, the function increases where 0< x < 2.

Multiple Choice

On what interval(s) is the function decreasing?

• -1 < x < 3

• x < -1 and x > 3

• x < 0 and x > 2

• 0 < x < 2

Open Ended

How can you tell where the graph of a function is decreasing?

A function is decreasing where its graph slopes downward from left to right, regardless of the arrows on the ends indicating the function continues.

Multiple Choice

Which choice is a relative maximum point for this function?

• (0, -1)

• (2, 3)

• (-1, 0)

• (3, 2)

Open Ended

Is there an absolute maximum for this function? If so, name it. If not, explain why not.

While (2, 3) is a relative maximum, there is no absolute maximum (or minimum) as the arrows on the ends of the function graph indicate that y values come from positive infinity and continue to negative infinity.

Multiple Choice

On what interval(s) is the function positive?

• x < 0

• x < -1

• x < -1 and x > 1

• x < -1 and x > 1

Open Ended

When looking at a graph of a function, how can you tell where the function is positive?

Open Ended

Why do we use x values when identifying where the graph of the function is positive?

1. Remember that y represents the value of the function (y = f(x)). Y is positive above the x-axis, therefore the function is positive where it lies above (not on) the x-axis.

2. Again, the x values determine which y-values we get (input vs output) so we want to know for which values of x do we get positive outputs for y.

Multiple Choice

On what interval(s) is the function negative?

• x < -1

• -1 < x < 1

• -1 < x < 1

• x < -1 and x > 1

Open Ended

When asked on what interval the function is negative, why is -1 < x < 1 incorrect?

The function is negative when its graph lies BELOW the x-axis (this is where the y-values are negative).  -1 < x < 1 is an incorrect interval for describing where the function is negative because it includes x= -1 and x = 1. The function is equal to zero at these values of x and zero is not negative.

Multiple Choice

What is the maximum value reached by this function?

• 1

• 2

• 3

• 4

Open Ended

What is the difference between a maximum point and a maximum value of a function?

1. When identifying the maximum point, you use coordinates to describe the point with the greatest y-value. Here the maximum point is (-1, 3).

2. When you identify the maximum value of a function, you want the highest value of y (remember that y represents the value of the function itself). Here the maximum of the function is 3.

Multiple Choice

What is the minimum value reached by this function?

• 0

• -2

• -3

• -4

Multiple Choice

Which interval choice is the domain of this function?

• [-4,4]

• [-3,3]

• [-4,-1)

• (-1,4]

Open Ended

What is the domain of a function?

The domain of a function is the set of all possible input (x) values. Here our domain ranges from -4 to 4 inclusive or [-4, 4].

Multiple Choice

Which interval choice is the range of this function?

• [-4,4]

• [-3,3]

• [-2,1)

• [-2,1]

Open Ended

What is the range of a function?

The range of a function is the set of all possible output (y) values. Here y can be any real number from -3 to 3 or [-3, 3].

Multiple Choice

If this function is referred to as f (x), which choice is f (-1)?

• 1

• -1

• 3

• both 1 and 3

Open Ended

What does f(-1) mean?

f(-1) represents the value of the function (y-value) where your input (x) value is -1.

Poll

How well do you feel you understand the features of graphed functions? [Please be honest]

• A lot! I have an excellent understanding of the different features of graphed functions.

• Fairly well. I have a solid understanding of most of the features, but still am a little confused about some things.

• Somewhat. I have a basic understanding of some things but am unsure or very confused about others.

• Almost none. I may know one or two basic features of graphed functions, but am very unsure/confused about most of the features.