# Midterm 1: Functions, Graphing, and Transformations

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Midterm 1: Functions, Graphing, and Transformations
JEOPARDY! Click Once to Begin Midterm 1: Functions, Graphing, and Transformations To change the question and answer slides, select the question or answer text box and type in your own questions and answers. To play, click on a question on the game board to go to that question. The house icon will take you to the game board and the question mark icon will take you to the answer slide. From the game board, the exclamation mark will take you to final Jeopardy. Template by Modified by Bill Arcuri, WCSD Chad Vance, CCISD

Here, There, and Everywhere
JEOPARDY! Real Love Here, There, and Everywhere Tell me “Y” The Word Magical Mystery Tour 100 100 100 100 100 200 200 200 200 200 300 Real Love: Real Line Here, There, and Everywhere: Translations Tell me “Y”: Real Plane, Functions (intercepts, symmetry, solutions) The Word: Word Problems Magical Mystery Tour: Grab Bag 300 300 300 300 400 400 400 400 400 500 500 500 500 500 Template by Modified by Bill Arcuri, WCSD Chad Vance, CCISD

Daily Double Graphic and Sound Effect!
DO NOT DELETE THIS SLIDE! Deleting it may cause the game links to work improperly. This slide is hidden during the game, and WILL not appear. In slide view mode, copy the above (red) graphic (click once to select; right click the border and choose “copy”). Locate the answer slide which you want to be the daily double Right-click and choose “paste”. If necessary, reposition the graphic so that it does not cover the answer text. Template by Modified by Bill Arcuri, WCSD Chad Vance, CCISD

Real Love-100 What the graph of the expression: |𝑥|<3 looks like
Template by Modified by Bill Arcuri, WCSD Chad Vance, CCISD

Answer What is an open circle or parenthesis at x=3 and x=-3 and shading between them? Template by Modified by Bill Arcuri, WCSD Chad Vance, CCISD

All values of 𝑥 that satisfy the inequality: 5𝑥−3 =2
Real Love-200 All values of 𝑥 that satisfy the inequality: 5𝑥−3 =2 Template by Modified by Bill Arcuri, WCSD Chad Vance, CCISD

Answer What are x=1 and x=1/5? Template by Modified by
Bill Arcuri, WCSD Chad Vance, CCISD

Real Love-300 In interval notation, the values of 𝑥 that satisfy the inequality: −1<3𝑥−3<6 Template by Modified by Bill Arcuri, WCSD Chad Vance, CCISD

Answer What is (2/3 , 3)? Template by Modified by
Bill Arcuri, WCSD Chad Vance, CCISD

The solution of the inequality 𝑥 2 −4 >0
Real Love-400 The solution of the inequality 𝑥 2 −4 >0 Template by Modified by Bill Arcuri, WCSD Chad Vance, CCISD

Answer What is −∞,−2 ∪ −2,2 ∪ 2,∞ ? Template by Modified by
Bill Arcuri, WCSD Chad Vance, CCISD

Solution of 𝑥(𝑥+2) 𝑥−2 ≤0 Real Love-500 Template by Modified by
Bill Arcuri, WCSD Chad Vance, CCISD

What is −∞,−2 ∪[0,2) Answer Template by Modified by
Bill Arcuri, WCSD Chad Vance, CCISD

Everywhere-100 It’s how the graph of 𝑓(𝑥) moves when you plot 𝑓(𝑥−1)
Template by Modified by Bill Arcuri, WCSD Chad Vance, CCISD

Answer What is one unit to the right? Template by Modified by
Bill Arcuri, WCSD Chad Vance, CCISD

Everywhere-200 Draw the graph of 𝑓(𝑥)= 𝑥 with correct intercepts and vertex. Template by Modified by Bill Arcuri, WCSD Chad Vance, CCISD

Everywhere-300 The exact vertex coordinates of the parabola described by 𝑓(𝑥)=𝑎 𝑥 2 +𝑏𝑥+𝑐 Template by Modified by Bill Arcuri, WCSD Chad Vance, CCISD

What is − 𝑏 2𝑎 , 4𝑎𝑐− 𝑏 2 4𝑎 ? Answer Template by Modified by
Bill Arcuri, WCSD Chad Vance, CCISD

Everywhere-400 The range of the function 𝑔 𝑥 = 2−𝑥 −1
Template by Modified by Bill Arcuri, WCSD Chad Vance, CCISD

Answer What is [−1,∞)? Template by Modified by
Bill Arcuri, WCSD Chad Vance, CCISD

Everywhere-500 The graph of 𝑓(𝑥)=|3𝑥−2| with correct vertex and intercepts. Template by Modified by Bill Arcuri, WCSD Chad Vance, CCISD

Answer What is Template by Modified by
Bill Arcuri, WCSD Chad Vance, CCISD

Tell me “Y”-100 It’s the exact distance in the plane between (-3,8) and (5,4) Template by Modified by Bill Arcuri, WCSD Chad Vance, CCISD

Answer What is (−3−5) 2 + (8−4) 2 = 64+16 = 80 ? Or 16∗5 =4 5 ?
Template by Modified by Bill Arcuri, WCSD Chad Vance, CCISD

Tell me “Y”-200 The shape or shapes you shade in when describing the region in the plane that satisfies 2≤|𝑥| Template by Modified by Bill Arcuri, WCSD Chad Vance, CCISD

Answer What is everything except a vertical strip from x=-2 to x=2?
Template by Modified by Bill Arcuri, WCSD Chad Vance, CCISD

Tell me “Y”-300 The center and radius of the circle 𝑥 2 + 𝑦−1 2 =1
Template by Modified by Bill Arcuri, WCSD Chad Vance, CCISD

Answer What are center (0,1) and radius 1? Template by Modified by
Bill Arcuri, WCSD Chad Vance, CCISD

Tell me “Y”-400 The center and radius of the circle 𝑥 2 + 𝑦 2 +4𝑦=−3
Template by Modified by Bill Arcuri, WCSD Chad Vance, CCISD

Answer Since 𝑥 2 + 𝑦 2 +4𝑦=−3 is the same as 𝑥−0 2 + 𝑦+2 2 =1, What are center (0,-2) and radius 1? Template by Modified by Bill Arcuri, WCSD Chad Vance, CCISD

Tell me “Y”-500 If f(x)=1/(x-1)+2, these are: the domain of 𝑓,
its intercepts, and the value of 𝑥 for which 𝑓(𝑥)=5 Template by Modified by Bill Arcuri, WCSD Chad Vance, CCISD

Answer All 𝑥≠1 or −∞,1 ∪ 1,∞ x-intercept (1/2,0) and y-intercept (0,1)
Template by Modified by Bill Arcuri, WCSD Chad Vance, CCISD

The Word-100 Calculus can be used to show that a ball thrown straight upward from the top of a building 128 ft high, with an initial velocity of 48 ft/sec, has a height of ℎ(𝑡)=−16 𝑡 2 +48𝑡+128 𝑡 seconds later. This is the time interval when the ball is at least 64 feet above the ground. Template by Modified by Bill Arcuri, WCSD Chad Vance, CCISD

Answer What is 0≤𝑡≤4 seconds? Template by Modified by
Bill Arcuri, WCSD Chad Vance, CCISD

The Word-200 An open rectangular box is to be made from a piece of cardboard 8 inches wide and 8 inches long by cutting a square size 𝑥-by-𝑥 from each corner and bending up the sides. Express the volume of the box as a function of size 𝑥 of the cutout. Template by Modified by Bill Arcuri, WCSD Chad Vance, CCISD

Answer What is 𝑉 𝑥 =𝑥 8−2𝑥 2 ? Template by Modified by
Bill Arcuri, WCSD Chad Vance, CCISD

The Word-300 A new computer workstation costs \$10,000. Its useful lifetime is 5 years, at which time it will be worth an estimated \$2,000. Using a linear decline method that’s legal under U.S. tax law, how much will the equipment be worth after 2.5 years? Template by Modified by Bill Arcuri, WCSD Chad Vance, CCISD

Answer The model of worth in dollars as a line is
𝑦−2000= 10000−2000 0−5 𝑥−5 =−1600(𝑥−5) so at 𝑥=2.5, we have 𝑦−2000=− −5 =4000 . What is \$6,000? Template by Modified by Bill Arcuri, WCSD Chad Vance, CCISD

The Word-400 The average weight 𝑊, in grams, of a fish in a particular pond depends on the total number 𝑛 of fish in the pond according to the model 𝑊(𝑛)=500−0.5𝑛 . Since the total fish weight production in the pond is 𝑛∙𝑊(𝑛), at what number is the maximum production reached? Template by Modified by Bill Arcuri, WCSD Chad Vance, CCISD

Answer Since 𝑛∙𝑊 𝑛 =500𝑛−0.5 𝑛 2 , the maximum occurs at 𝑛=− 𝑏 2𝑎 =− 500 −1 =500 fish in the pond. Template by Modified by Bill Arcuri, WCSD Chad Vance, CCISD

The Word-500 The manager of a manufacturing company finds it costs \$3200 to produce 100 units of product per day and \$9600 to produce 500 units per day. Assuming the cost function 𝐶(𝑥) is linear, what does the slope of 𝐶(𝑥) represent? Template by Modified by Bill Arcuri, WCSD Chad Vance, CCISD

Answer What is the number of dollars to produce one unit?
Template by Modified by Bill Arcuri, WCSD Chad Vance, CCISD

Tour-100 What is the domain of 𝑠 𝑥 = −𝑥 ? Template by Modified by
Bill Arcuri, WCSD Chad Vance, CCISD

Answer What are reals less than or equal to zero? or {𝑥:𝑥≤0} or (−∞,0]
Template by Modified by Bill Arcuri, WCSD Chad Vance, CCISD

Tour-200 What is a visual way to determine whether a graph represents a function? Template by Modified by Bill Arcuri, WCSD Chad Vance, CCISD

Answer What is the Vertical Line Test? Template by Modified by
Bill Arcuri, WCSD Chad Vance, CCISD

Tour-300 Given that 𝐴=𝜋 𝑟 2 for a circle, this is the area of the region that lies outside the circle 𝑥−1 2 + 𝑦 2 =1 and inside the circle 𝑥−2 2 + 𝑦 2 =4 Template by Modified by Bill Arcuri, WCSD Chad Vance, CCISD

Answer What is 𝐴=𝜋 (2) 2 −𝜋 1 2 =3𝜋? Template by Modified by
Bill Arcuri, WCSD Chad Vance, CCISD

Tour-400 All symmetries of the function 𝑦= 𝑥 4 + 𝑥 2 .
Template by Modified by Bill Arcuri, WCSD Chad Vance, CCISD

Answer What is y-axis symmetry (evenness)? Template by Modified by
Bill Arcuri, WCSD Chad Vance, CCISD

Tour-500 Find the domain of the function: 𝑓 𝑥 = 𝑥−1 𝑥 2 +3𝑥+2
Template by Modified by Bill Arcuri, WCSD Chad Vance, CCISD

Answer What is −2,−1 ∪[1,∞)? -2 -1 1 Template by Modified by
Bill Arcuri, WCSD Chad Vance, CCISD

That’s All Right (Mama)
Final Jeopardy That’s All Right (Mama) Please place your team wager now. Template by Modified by Bill Arcuri, WCSD Chad Vance, CCISD

Final Jeopardy The line perpendicular to 𝑦=2𝑥−1 passing through the point (3,1). Template by Modified by Bill Arcuri, WCSD Chad Vance, CCISD

Final Jeopardy What is 𝑦=− 1 2 𝑥+ 5 2 ? Template by Modified by
Bill Arcuri, WCSD Chad Vance, CCISD