Function Sparks Warm Up
Algebra 1 Daily Starter
Function Sparks Warm Up
Name:
Date:
Period:
Quick Recall: Direct variation forms a proportion: \( \frac{y_1}{x_1} = \frac{y_2}{x_2} = k \). Domain = inputs (\(x\)); Range = outputs (\(y\)).
Target: 6–8 min
Problem 1
Direct Variation & Proportions
[ 5 Points ]
The distance \( d \) a hybrid car travels varies directly with the gallons of fuel \( g \) used. The vehicle travels \( 168\text{ miles} \) on \( 4\text{ gallons} \) of gasoline.
Part A: Set Up the Proportion
Set up a proportion to find the distance \( d \) the car can travel on \( 9\text{ gallons} \).
Fill in each value:
=
Ratio: \( \frac{\text{miles}}{\text{gallons}} = \frac{\text{miles}}{\text{gallons}} \)
Part B: Cross-Multiply & Solve
Show your cross-multiplication steps to solve for \( d \).
Distance for 9 gallons: \( d = \) miles
Part C: Constant of variation (Unit Rate): \( k = \) mpg
Direct Variation Equation:
Problem 2
Domain & Range from a Continuous Graph
[ 5 Points ]
Examine the graph of continuous function \( f(x) \) shown on the coordinate plane below. Note the solid and open circle endpoints carefully.
x y -4 -2 2 4 4 2 -2 -4 (0, -3) (-4, 4) (5, 2)
Part A: Domain (Inputs)
Determine the set of all \( x \)-values covered by the graph.
Inequality: Interval: [ ___ , ___ )
Part B: Range (Outputs)
Determine the set of all \( y \)-values covered (minimum to maximum).
Inequality: Interval: [ ___ , ___ ]
Part C: Function Test
YES NO
Justify your choice using the Vertical Line Test:
Self-Confidence Check:
1: Need Review 2: Almost There 3: Got It! 4: Mastered
Total Score: / 10
