MATH 130 · Sections 2.1, 2.2, 2.4

Functions and Coordinate Geometry

Relations, function notation, domain and range, distance, midpoint, and circles

50–55 minutes · Offline capable · Quiz 3 · Sep 16 at 2:10 PM

Learning roadmap and pacing

  1. 1

    decide whether a relation defines a function

  2. 2

    evaluate functions and report domain and range

  3. 3

    use midpoint and distance formulas accurately

  4. 4

    interpret and write the standard equation of a circle

Canvas pacing anchor

Quiz 3 · Sep 16 at 2:10 PM

ALEKS Sections 2.1, 2.2, 2.4 due Sep 16 at 2:10 PM

Coverage note

This deck is the sequential study path. Official quiz and test coverage can be adjusted in Canvas or in class.

Activate · 2 minUnit 1 sequence

Entrance retrieval

4 minutes · no notes
  1. Does $\{(1,4),(2,4),(1,7)\}$ define $y$ as a function of $x$?
  2. Evaluate $f(-2)$ for $f(x)=x^2-3x$.
  3. Find the midpoint of $(2,-3)$ and $(8,5)$.

Activate · 4 minUnit 1 sequence

A function gives each input one output

Function

Repeated outputs are allowed. Repeated inputs must keep the same output.

Not a function

One input is paired with two different outputs.

Graph test

A vertical line may intersect a function graph at most once.

Explain · 5 minUnit 1 sequence

Function notation names an input-output rule

For $f(x)=2x^2-5x+1$, find $f(-3)$.

  1. Replace every $x$ with $(-3)$.
  2. $2(-3)^2-5(-3)+1=18+15+1$.
  3. $f(-3)=34$.

Model · 5 minUnit 1 sequence

Domain comes from permissible inputs

1

Polynomial: all real inputs.

2

Rational expression: exclude denominator zeros.

3

Even root: require radicand $\ge0$.

For $g(x)=1/(x-4)$, domain is $(-\infty,4)\cup(4,\infty)$.

Explain · 5 minUnit 1 sequence

Coordinate formulas are organized substitutions

$M=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})$

$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Structure check

Midpoint averages; distance subtracts, squares, adds, and square-roots.

Explain · 5 minUnit 1 sequence

A circle records center and radius

Write the circle with center $(4,2)$ and radius $5$.

  1. Use $(x-h)^2+(y-k)^2=r^2$.
  2. Substitute $h=4$, $k=2$, $r=5$.
  3. $(x-4)^2+(y-2)^2=25$.

Model · 5 minUnit 1 sequence

You try: connect representation and geometry

Work first · then reveal

  1. For $f(x)=3x-7$, solve $f(x)=11$.
  2. State the domain of $h(x)=\sqrt{x+5}$.
  3. For $A(-1,2)$ and $B(5,10)$, find midpoint and distance.

Practice · 5 minUnit 1 sequence

Quiz 3 checkpoint: readiness check

Quiz 3 checkpoint
Closed notes · show complete work
  1. Explain why $\{(-1,2),(0,4),(2,4)\}$ is a function.
  2. Find the domain of $p(x)=1/(x^2-9)$.
  3. Find midpoint and distance for $(0,0)$ and $(6,8)$.
  4. Identify the center and radius of $(x+2)^2+(y-5)^2=16$.

Assess · 8 minUnit 1 sequence

Exit ticket and next step

Before you leave
  1. Name one skill you can now complete without notes.
  2. Name one error pattern to watch.
  3. Schedule the next short practice before the checkpoint.
Next step

Next: Unit 1D — quadratic equations, applications, and extrema

Synthesize · 3 minUnit 1 sequence