Linear Functions and Graph Analysis Study Notes

Complete the three graphs and remaining packet pages before working on the review guide.
The test is scheduled for Thursday of next week.
Delta bound practice and delta knot are posted online for additional review.

Initial Value (Y-intercept): The starting value is $\$4.07$ or $\$4.75$ , providing the ordered pair $(0, 4.75)$ .
Rate of Change: Adds $\$1.25$ for each week ( $x$ ).
Model Equation: Written as $f(x) = 1.25x + 4.75$ .
Variable Classification: Continuous, as partial dollar amounts such as $\$0.50$ are valid.
End Behavior: As $x \rightarrow \infty$ (moving right), $f(x) \rightarrow \infty$ (moving upward).
Intervals: Positive when x > 0 and never negative.
Domain and Range: Domain starts at $0$ and extends infinitely or to an upper bound of $7000$ ( $[0, 7000]$ or $[0, \infty)$ ). Range starts at $\$4.75$ up to $7000$ ( $[4.75, 7000]$ ).

Fill Rate: Water fills at a rate of $20\,\text{gallons per minute}$ .
Sub-unit Calculation: At $30\,\text{seconds}$ ( $0.5\,\text{minutes}$ ), the volume is $10\,\text{gallons}$ .
Variable Classification: Continuous, as time measured in decimal seconds (such as $28\,\text{seconds}$ ) yields continuous gallon values.

Question on Table Setup: A student asked Mister Lumpkin how to construct the table values from copied notes.
Response: Start with $x = 0$ at $\$4.75$ , then increment $x$ by $1$ each week while adding $\$1.25$ to the total.
Question on Negative Values: A student inquired why negative values are not represented on the graph.
Response: A negative number of days cannot exist in this scenario, so the y-intercept $(0, 4.75)$ serves as the starting point.
Discussion on Past Teacher: Students discussed Miss Vickery, debating whether she retired or was fired during the previous year.
Classroom Remarks: Brief exchanges occurred involving Lacey regarding Obamotration and Brian.