Quadratic equations Questions and Answers

Evaluate the expression without using a calculator log 226

Evaluate the expression without using a calculator 1 327 log 31 1

In the diagram AB ACAB AC below CD 8CD 8 and AD AEAD AE MM is the midpoint of BEBE and LABE 190 2CAD 43 2AEB 24 ZABE 19 CAD 43 AEB 24 Use this information to calculate the length of AMAM B A M D 411 E

5 Inverse Functions If two functions f x and g x are inverses then what will f g x and g f x both equal

f is a polynomial function with degree 30 and leading coefficient 16 The graph of f has at most A turning points

4 Listm Select the graph that best matches the given function g 1 4 O 10 8 64 2 L6 10 10 2 10 8 6 4 73 2 4 6 8 10

Graph f x O A and g x log 1 8x in the same rectangular coordinate system Choose the correct graph below G B Q G O P A

0 2 1 Let A 5 1 7 42 5 AB and B 3 3 6 4 7 6 Find AB if it is defined Otherwise click on Undefined 010 8 10 000 8 909 gogol 8 8 8 DOD AAA JUB

Evaluate the expression without using a calculator log 2256

Write in logarithmic form 100 8 2 3 The logarithmic form is

The function T R R is defined by Show that I is linear 1 T 12 13 Yes 372 503 521 523 To make sure you are on the right track you should answer the following questions a Is the domain of T a known vector space Yes b Is the codomain of T a known vector space Yes c Does T preserve vector addition Yes d Does T preserve scalar multiplication for all 1 728 22 ER 3

4 10 marks Given the following information about a sinusoidal function complete each of the following tables a MAAAAAA 11 2 Domain Range Amplitude Period 311 2 11 TT 512

9 Which of the following statements are true for the given hyperbola CIRCLE ALL THAT APPLY x 6 y 2 1 18 7 a The center is located at 6 2 b The hyperbola has a vertical transverse axis c The hyperbola has a horizontal transverse axis d The foci are located at 6 11 2 e The foci are located at 11 2 and 1 2

The domain of the piecewise function is 0 00 a Graph the function b Use your graph to determine the function s range f x 2x if x 0 2x if x20

Which ordered pair makes both inequalities true y 2x 3 y x 2 0 0 O 0 1 2 J J J K L 1 22

Is the function shown on the graph below one to one 6 10 N

Find the inverse of f x 4x for x 0 The inverse function is f x 1

2x 12 Draw a graph of f x by first placing the horizontal and vertical asymptotes then plotting 2x 4 an additional point on the graph 5 4 3 2 1 Clear All Draw 5 4 3 2 1 1 2 3 S A or w

The graph of a function f is given On the same axes sketch the graph of f1 Use a dashed line for the inverse function OA N OB 57 O C O D

Let A x f t dt with f x shown in the graph below 5 4 3 2 1 1 2 3 At what x values does A x have a local max x At what x values does A x have a local min x Restrict your answers to values 0 x 6 5

Find the inverse of the function f x 3x 4 3 X 4 3 O B 1 1 x 3 x 4 X F OD Not a one to one function O A f1 x 3 O c f 1 x 3 4

th 82 14 24 2 The quotient ist remainder is V r

cot given tan 3 B 2 5 2 cos B 0

Draw the graph of f x 4 2 10 9 8 7 6 Clear All Draw 5 4 3 2 1 10 9 8 7 6 5 4 3 2 7 ON 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10

The pointer on a voltmeter is 6 centimeters in length see figure Find the number of degrees through which the poin when it moves 2 5 centimeters on the scale Round your answer to two decimal places 6 cm

3 sina 11 7 with a in quadrant I and sin with in quadrant II

For a particular commodity the demand function is q a Find e when p 16 Preview b Is demand elastic inelastic or unit elastic Select an answer y 4000 p5

4 1 4 2 why not You may use a calculator for matrix reduction but interpret the result n your own words 2 7 1 8 Let A Is the vector 7 in the column space of A Show why or 3

Find the values of the indicated functions Given cot 8 0 628 find sec 0 and sin 0 sec 0 Do not round until

Directions In 1 3 use the given information to find cos a B and cos a B 5 with in quadrant III 1 cosa 13 with a in quadrant IV and sin 8

Find the exact value of cos csc 3 2 cot 2

In the triangle shown we can find the angle as follows a 8 sin 1 b 0 cos 1 c 8 tan 1 15 12 0 4 1 25 Points DETAILS SPRECALC7 6 4 004 To find sin cos we let cos A 9 sin cos and complete the right triangle below We find that sin cos

Let A x f t dt with f x shown in the graph below 5 4 3 2 1 Z 2 3 5 At what x values does A x have a local max x At what x values does A x have a local min x Restrict your answers to values 0 x 6 5

8 In the figure below the measure of arc BD is 106 degrees the measure of arc DF is 96 degrees the measure of arc FH is 138 degrees and the measure of arc HB is 20 degrees Find the measure of FPD 3 points P B C E I

Find the area of the shaded region enclosed in a semicircle of diameter 8 centimeters The length of the chord AB s 4 centimeters Hint Triangle ABC is a right triangle The area is approximately square centimeters Do not round until the final answer Then round to two decimal places as needed 4 8 B Q

Let f x 6x 5 and g x f g x 1 X X 6x 5 Simplify your answer Find f g x f g x fg x and f g x Simplify your answer x Give the domain of each

Use the Trapezoidal rule to estimate the integral fex dx taking t number 10 intervals

1 Factor the polynomial completely and find all of its zeroes p x x 4 x 2 2

1 Let f x 6x 5 and g x Find f g x f g x fg x and X fg x 6x 5 X Simplify your answer x x 6x 5 Simplify your answer 5 6 Type your answer in interval notation The domain of f g is 5 6 Type your answer in interval notation The domain of f g is 5 3 00 6 Type your answer in interval notation The domain of fg is The domain of is g Type your answer in interval notation x Give the domain of each

The graph of an exponential function f is given to the right with three points labeled Sketch the graph of 11 by hand laboling three points on the graph For also state the domain the range whether it increases or decreases on its domain and the equation of its vertical asymptote Do not use a calculator CHESS What is the point on corresponding to the point 1 10 on the graph off Type an ordered pair using intogers or fractions What is the point on f corresponding to the point 0 1 on the graph of 1 0 Type an ordered pair using integers or fractions What is the point on t corresponding to the point of on the graph of 404 4 1101 140030 40 41

9 Find sin cos tan given cos 2 119 169 and terminates in Q IV

Which interval or inequality below matches the graph below 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7

7 Given the function f x log x 2 3 a Find the domain of f b Graph f

2 Extraneous Solutions For each equation below substitute the solutions back into the equation to determine which one is the extraneous solution a x 5 x 1 x 1 or x 4 b 3x 2 2 x x 1 or x 6

1 Consider the following IBVP for the heat equation on the line Ut 502x u x 0 f x where f x 0 x t 0 1 for 2 3 for 3 x 4 for x 4 a Find the solution and express it in terms of error functions b Sketch the graph of u x t when t 0 t 0 01 and t 0 1 c Using the formula that you found in part a check that lim u 3 5 t f 3 5 showing all work 0

First find f g f g fg and Then determine the domain for each function g f x 3x 7 g x x 4 f g x Simplify your answer What is the domain off g 00 00 0 00 31 1 00 1 U 21 00 f g x What is the domain off g 00 77 U 7 17 00 11 2 Simplify your answer 00 0 00 0 00 00 fg x What is the domain of fg 0 00 00 0 00 4 U 4 00 x What is the domain of g O 00 00 4 00 0 00 O 0 4 U 4 00

Consider the function h x 2 What is the vertex of h h has a Select an answer of What is the equation of the line of symmetry of h The intercept s of h is are 3x The y intercept of h is 11 2 Graph h x 10 9 8 7 6 Clear All Draw 9 7 6 5 3 2 2 3 S 6 7 8 7 8 9 10 AVO For this question give all rational answers as fractions or integers and all irrational answers rounded to 2 decimal places

Solve 4x 8 2 12 The answer has the form O A U B O A B State your solution using interval notation like aboy

6 cos 20 and In what quadrant does 2 3 terminate sin 23 given tan 3 sin 0

Extra Credit Students in a fifth grade class were given an exam During the next 2 years the same students were retested several times The average score was given by the model f t 94 3 log t 1 0 t 24 where t is the time in months Round answers to at least 1 decimal point a What is the average score on the original exam 94 b What was the average score after 6 months 70 71 c What was the average score after 18 months 58 72 I X x