1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Kipish [7]
3 years ago
12

suppose f(x)=3x+5. describe how the graph of each function compares to f. 1) g(x)=f(x)+12 2) h(x)=f(x)-7 3) g(x)=f(x=8) 4) h(x)=

f(x-14) 5) g(x)=4f(x) 6) g(x)=f(5x)
Mathematics
1 answer:
Lubov Fominskaja [6]3 years ago
6 0

1)

g(x) = f(x)+12 represents translating f(x) 12 units up to get g(x). This is because y = f(x), so we're effectively adding 12 to each y coordinate of the points on f(x) to have them move to the points on g(x).

note: the term "translating" is another way of saying "shifting" or "sliding".

===================================================

2)

h(x) = f(x)-7 means translating f(x) 7 units down to get h(x). We use the same reasoning as in problem 1. The general form is h(x) = f(x)+k, and in this case, k = -7. The negative k value tells us to shift down.

===================================================

3)

g(x) = f(x+8) means we translate 8 units to the left. The general template is g(x) = f(x-h). If h > 0, then we shift right. If h < 0, then we shift left. The amount that is shifted is equal to the absolute value of h.

===================================================

4)

h(x) = f(x-14) tells us to shift f(x) 14 units to the right. Same idea as problem 3, but now h = 14.

===================================================

5)

g(x) = 4*f(x) means we vertically stretch f(x) by a factor of 4. Since y = f(x), we are effectively doing g(x) = 4*f(x) = 4*y, which pulls the y coordinates upward by a factor of 4. A point like (1,2) will jump to (1,8) after multiplying the y coordinate by 4.

===================================================

6)

g(x) = f(5x) tells us to horizontally compress f(x) by a factor of 5. The general template is g(x) = f(a*x) where the 'a' determines horizontal stretching or compression. If 0 \le a \le 1, then we have horizontal stretching going on. If a > 1, then we'll have horizontal compression.

You might be interested in
-3.8x - 5.9x = 223.1
katrin2010 [14]

Answer:

x=-23

Step-by-step explanation:

-3.8x-5.9x=223.1

-9.7x=223.1

x=223.1/-9.7

x=-23

5 0
3 years ago
Read 2 more answers
Find the length of a rectangle with a diagonal of 10 and a height of 8.
Dmitry_Shevchenko [17]

Answer:

The length of the rectangle is 6.

Step-by-step explanation:

Given: The diagonal of a rectangle is 10 and the height is 8.

Please understand, that a diagonal, divides the rectangle into two tringles.

To find the length of the rectangle, you can use Pythagoras on one of the right sided triangles, because the length of the triangle, is also the length of the rectangle!

<em>EXTRA:</em>

<em>If</em><em> you know the special 3 4 5 triangle, a so called Pythagorean Triple, then you can "see" the simularity between the numbers.</em>

<em>Instead of 5, a diagonal of 10 is given (factor of 2 bigger).</em>

<em>Instead of 4, the height of 8 is given (factor of 2 bigger</em><em>)</em><em>.</em><em> </em><em>By scaling the Pythagorean Triple 3 4 5 by a factor of 2, you get the numbers 6 8 10. Could it be, that the number we need to find, is six?</em>

Try to verify, by calculating the missing number (which is the length of the rectangle we are looking for).

a² + b² = c²

a = length (and is unknown)

b = height = 8

c = hypothenusa/diagonal = 10

Substitute the numbers given:

a² + 8² = 10²

Subtract 8² left and right of the = sign.

a² +8² -8² = 10² - 8²

a² + 0 = 100 - 64

a² = 36

a = + - √36

a = + - 6

<em>EXTRA</em><em>:</em>

<em>You</em><em> can ignore the -√36 = -6 part of the solution, because a length of -6 has no meaning here.</em>

a = 6

So, the length of the triangle is 6 and thus, the length of the rectangle is also 6.

8 0
3 years ago
I Need Help thanks <br>:)?​
Feliz [49]

Answer:

6)  x = 40.5

8)  x = 16.5

Step-by-step explanation:

6) 45/x = 20/18

simplify and cross-multiply to get:

45/x = 10/9

10x = 405

x = 40.5

8) 22/8 = x/6

11/4 = x/6

4x = 66

x = 33/2

x = 16.5

8 0
2 years ago
How to solve 3/2 = 9/10k (in fraction form). Please show work
antoniya [11.8K]
3/2 and 9/10. Look at the denominators. 2 times what number equals 10. That number would be 5. So if you multiply the first fractions denominator by 5 you get 10. Do the same to the top. you get a new fracrion which is 15/10. Add normally. 15/10 + 9/10 = 24/10. In lowest terms it is 2 2/5 (2 wholes and 2 out of 5)
5 0
3 years ago
Read 2 more answers
PLEASE HELP MEEEEEEEEEEEEEEEEEE!!!!!!!!
victus00 [196]
F = 41
E = 90
D = 49
from D to E is 55
then E to F also known as X = 36.08 or 41.51
6 0
3 years ago
Other questions:
  • Is 3/4 and 3/8 equivalent fractions and why? Thanks
    12·2 answers
  • 5.75% in decimal form
    11·2 answers
  • What number makes (x+1)(x+2) equal 9
    15·1 answer
  • The wingspans of Rodrigues fruit bats are normally distributed, with a mean of 82.5 centimeters and a standard deviation of 2.5
    6·1 answer
  • What is -2(4g-3)=30 I can't figure it out so I need so help
    5·1 answer
  • A container is 80​% filled with liquid. The container holds 1,180 gallons of liquid. How many gallons of liquid are needed to fi
    5·2 answers
  • Convert the following equation<br> into standard form.<br> y = 2x – 4<br> -2x + y = [?]
    10·2 answers
  • im basically just gonna keep putting up sum1 hmu till sum1 with an interesting conversation talks 2 me l-m-a-oooooo
    13·1 answer
  • Please do 25 and 26 or atleast one
    14·1 answer
  • What is the diameter of a sphere with a volume of 18174 ft 3 , 18174 ft 3 , to the nearest tenth of a foot?
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!