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2 years ago

Lee graphs the function y=2x2+1 y = 2 x 2 + 1 . Which statement explains whether the function is linear or not linear?

Mathematics

1 answer:

Sveta_85 [38]2 years ago

4 0

Answer:

Step-by-step explanation:it in slope intercept form

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Determine if the table shows a linear or an exponential function

____ [38]

Answer:

<em>The table shows an exponential function</em>

Step-by-step explanation:

<u>Linear vs Exponential Functions</u>

A linear function is written as:

$y=mx+b$

where m and b are constants.

If a table contains a linear function, then for each pair of ordered pairs (x1,y1) and (x2,y2), the value of m must be constant.

The slope can be calculated as:

$\displaystyle m=\frac{y_2-y_1}{x_2-x_1}$

An exponential function is written as:

$y=y_o.r^x$

Where r is the ratio and yo is a constant.

If a table contains an exponential function, for two ordered pairs (x1,y1) and (x2,y2), the value of r must be constant.

The ratio can be calculated as:

$\displaystyle r=\sqrt[x2-x1]{\frac{y2}{y1}}$

Calculate the slope for (0,4) and (1,2):

$\displaystyle m=\frac{2-4}{1-0}=-2$

Calculate the slope for (1,2) and (2,1):

$\displaystyle m=\frac{1-2}{2-1}=-1$

Since the slope is not the same, the function is not linear.

Now calculate the ratio for (0,4) and (1,2)

$\displaystyle r=\sqrt[1-0]{\frac{1}{2}}$

The radical of index 1 is simply equal to its argument:

$\displaystyle r=\frac{1}{2}$

Now calculate the ratio for (0,4) and (2,1)

$\displaystyle r=\sqrt[2-0]{\frac{1}{4}}$

$\displaystyle r=\sqrt{\frac{1}{4}}$

$\displaystyle r=\frac{1}{2}$

Testing other points we'll find the same ratio, thus the table is an exponential function

4 0

2 years ago

Read 2 more answers

I need help with these two

Zinaida [17]

1. Adding all the responses together, we get the total number of responses is 24. The number of people who chose a genre that wasn't mystery was 7 for science fiction, 6 for history, and 3 for biographies. This means we will have 3 fractions before reducing. 7/24, 6/24, and 3/24. 7/24 is in simplest form, but 6/24 and 3/24 can be reduced. 6/24 can be 3/12 and 1/4. 3/24 can be 1/8. The answer will be to circle 7/24, 6/24, 3/12, 1/4, 3/24, or 1/8.

2. Plot the points given, and mirror them for point B and C to form the figure. When connecting them, the resulting figure should look extremely similar to the picture given.

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2 years ago

5 of 16

nlexa [21]

Answer:

Step-by-step explanation:

50 X 62% = 31

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2 years ago

Read 2 more answers

What is the slope of the line?

drek231 [11]

Answer:

Step-by-step explanation:

2/3

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2 years ago

Donner l'écriture scientifiques des nombres ci-dessous

rjkz [21]

Answer:

Step-by-step explanation:

salut :

500 000 000= 5× 10^8

650 000= 6,5 ×10^4

58 400 000 000= 5.84 ×10^8

0,000 6= 6×10^-4

0,000 032= 3.2 ×10^-4

0,000 000 072 3= 7.23 × 10^-8

0,000 000 072 3=7,23×10^-7

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3 years ago