Mathematics, 29.12.2019 13:31 abby6213

Do not use your calculator for parts 1 through 4.

let f be the function defined as follows:

{ 3-x, for x < 1
f(x) = { ax^2 + bx, for 1 ≤ x < 2
{ 5x-10, for x ≥ 2

where a and b are constants

the equation in written form: f of x equals the piecewise function three minus x for x is less than one, a x squared plus b x for one is less than or equal to x is less than two, and five x minus ten for x is greater than or equal to two where a and b are constants.

1. if a = 2 and b = 3, is f continuous at x = 1? justify your answer.

2. find a relationship between a and b for which f is continuous at x = 1.
hint: a relationship between a and b just means an equation in a and b.

3. find a relationship between a and b so that f is continuous at x = 2.

4. use your equations from parts (ii) and (iii) to find the values of a and b so that f is continuous at both x = 1 and also at x = 2?

5. graph the piece function using the values of a and b that you have found. you may graph by hand or use your calculator to graph and copy and paste into the document.

Answers: 1

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Answers

You have to understand how piecewise functions first
I hope you do because I won't be explaining it here

1.
if it is continiuous at x=1 then the part of the function that approaches 1 from the left is the same value
so we have f(x)=3-x for x<1, so evaluate it for x=1,
we would get 3-1=2
so
if a=2 and b=3

f(x)=2x²+3x
for x=1, we get 2+3=5

it approaches 2 from the left but equals 5
2≠5
so it is not continuous because it doesn't approach the same value at x=1

2.
alright
so we established that it should approach 2 because we had the f(x)=3-x
so
f(1)=2=ax²+bx
2=a+b
the relationship is 2=a+b

3.
same as before, but use the other function, the one that is defined at x≥2
5x-10, 5(2)-10, 10-10, 0
it approaches 0
so
we must find one such that f(x)=0 for x=2 with the ax²+bx
0=a(2)²+b(2)
0=4a+2b
if we minus 2b both sides
-2b=4a
divide by 2
-b=2a
add b both sides
0=2a+b

4.
2=a+b
0=2a+b

2=a+b
minus b both sides
2-b=a
subsitute
0=2a+b
0=2(2-b)+b
0=4-2b+b
0=4-b
b=4

sub back
2-b=a
2-4=a
-2=a

a=-2
b=4

5.
graph f(x)=-2x²+4x from x=1 to x=2 and put a closed dot at (1,2) and an open dot at (2,0)

Answer from: Quest

because 1.2 isnt half of 6 duh

Answer from: Quest

see below

step-by-step explanation:

7. there are 10 data points in the set. the middle point is between 5 and 6. the middle point in the top half is 8 and the middle point in the bottom half is 3. to find the iqr , take point 8 and subtract point 3

mid term point 8 = 100 point 3 = 88

iqr = 100-88 = 12

final point 8 = 93 point 3 = 78

iqr = 93 - 78 = 15

the final has the greatest iqr

6. b - there is a high data value that causes the data set to be asymmetrical for the males: the data for males are high and asymmetrical . there is an outlier for the males that skews the data

5. the iqr is a better measure of spread for the movies and basketball games. since the basketball game has an outlier, we do not want to use standard deviation for measurement.

3. the exam median is much higher than the class median. the median line is farther to the right on the exams

2. there is no way to tell what the means are from the box and whisker plots.

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Do not use your calculator for parts 1 through 4.

let f be the function defined as follo...

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