P3.1: Graph features

Last updated about 4 years ago

8 questions

Note from the author:

Instructions

P3.1: Graph features

Last updated about 4 years ago

8 questions

Note from the author:

You will use Desmos for this assignment.

When you type a word (minimum, maximum, increasing, decreasing) type just the word, no spaces or punctuation.

You may type "infinity" and "-infinity" without quote marks if the infinity symbol is giving you issues.

This video explains end behaviors.

Instructions

You will use Desmos for this assignment.

When you type a word (minimum, maximum, increasing, decreasing) type just the word, no spaces or punctuation.

You may type "infinity" and "-infinity" without quote marks if the infinity symbol is giving you issues.

This video explains end behaviors.

Consider the quadratic function:  f(x) = x^{2}+4x-6

The vertex is at _______ (use (x, y) format, one space after the comma).
The vertex is a _______  (minimum, maximum).
The axis of symmetry is _______ (your answer should include an equal sign).
The function is increasing on the interval _______ (use (#, #) format. For \infty, copy/paste from here).
The function is decreasing on the interval _______ 
As x \rightarrow \infty, f(x) \rightarrow _______ 
As x \rightarrow -\infty, f(x) \rightarrow _______ 

Consider the quadratic function:  f(x) = (x-2)^{2}+4

The vertex is at _______ (use (x, y) format, one space after the comma).
The vertex is a _______  (minimum, maximum).
The axis of symmetry is _______ (your answer should include an equal sign).
The function is increasing on the interval _______ (use (#, #) format. For \infty, copy/paste from here).
The function is decreasing on the interval _______ 
As x \rightarrow \infty, f(x) \rightarrow_______ 
As x \rightarrow -\infty, f(x) \rightarrow_______ 

Consider the quadratic function:  f(x) = -3x^{2} + 6x

The vertex is at _______ (use (x, y) format, one space after the comma).
The vertex is a _______  (minimum, maximum).
The axis of symmetry is _______ (your answer should include an equal sign).
The function is increasing on the interval _______ (use (#, #) format. For \infty, copy/paste from here).
The function is decreasing on the interval _______ 
As x \rightarrow \infty, f(x) \rightarrow _______ 
As x \rightarrow -\infty, f(x) \rightarrow _______ 

Consider the quadratic function:  f(x) = (x+1)^{2}-3

The vertex is at _______ (use (x, y) format, one space after the comma).
The vertex is a _______  (minimum, maximum).
The axis of symmetry is _______ (your answer should include an equal sign).
The function is increasing on the interval _______ (use (#, #) format. For \infty, copy/paste from here).
The function is decreasing on the interval _______ 
As x \rightarrow \infty, f(x) \rightarrow _______ 
As x \rightarrow -\infty, f(x) \rightarrow _______ 

Consider the square root function:  f(x) = \sqrt{x+3}

The vertex is at _______ (use (x, y) format, one space after the comma).
The domain is _______  (use interval notation.  For \infty, copy/paste from here.)
The range is _______  (use interval notation).
This function is _______ (increasing, decreasing).

Consider the square root function:  f(x) = -\sqrt{x-1}+2

The vertex is at _______ (use (x, y) format, one space after the comma).
The domain is _______  (use interval notation.  For \infty, copy/paste from here.)
The range is _______  (use interval notation).
This function is _______ (increasing, decreasing).

Consider the square root function:  f(x) = 2\sqrt{x+5}+6

The vertex is at _______ (use (x, y) format, one space after the comma).
The domain is _______  (use interval notation.  For \infty, copy/paste from here.)
The range is _______  (use interval notation).
This function is _______ (increasing, decreasing).

Consider the square root function:  f(x) = \frac{1}{3}\sqrt{1-x}+2

The vertex is at _______ (use (x, y) format, one space after the comma).
The domain is _______  (use interval notation.  For \infty, copy/paste from here.)
The range is _______  (use interval notation).
This function is _______ (increasing, decreasing).