183k views
5 votes
PLEEEEEAAASEEE HELLLPPPPPPP

PLEEEEEAAASEEE HELLLPPPPPPP-example-1

1 Answer

4 votes

Explanation:

a linear function grows at a constant rate, with equal increments added or subtracted over the same interval of x, while an exponential function involves a constant multiplier that drives an increase or decrease over the same interval of x.

in our examples here the intervals of x are always 1 (1 to 2 to 3 to 4). so, we don't need to bother to norm the intervals to each other.

so, we can simply look at the differences of the f(x) data points.

in the first example the difference from 5 to 7 is 2.

the difference of 7 to 9 is 2. and the difference of 9 to 11 is 2.

so, whenever x is increased by 1, f(x) increases exactly by 2. therefore, clearly, we add the constant 2 every time.

this is a linear function.

f(x) = 2x + 3

the added constant is the factor of x, also called the slope of the line.

in the second example we see

2×2 = 4, 4×2 = 8, 8×2 = 16

so, clearly we multiply by the constant factor 2.

this is therefore an exponential function.

f(x) = 2^x

the multiplied constant is the base of the exponent.

in the third example we see that we always multiply by the constant factor ½.

½ = 0.5

0.5 × ½ = 0.25

0.25 × ½ = 0.125

0.125 × ½ = 0.0625

this is therefore an exponential function.

f(x) = (½)^x

the multiplied constant is again the base of the exponent.

in the fourth example we see that 0.03 is added constantly.

0.04 + 0.03 = 0.07

0.07 + 0.03 = 0.1

0.1 + 0.03 = 0.13

this is a linear function.

f(x) = 0.03x + 0.01

the added constant is the factor of x, also called the slope of the line.

in the fifth example we see that -4 is added constantly.

-6 - 4 = -10

-10 - 4 = -14

-14 - 4 = -18

this is a linear function.

f(x) = -4x - 2

the added constant is the factor of x, also called the slope of the line.

in the sixth example we see that there is no constant being added

1 + 15 = 16

16 + 65 = 81

but also no constant multiplication factor

1 × 16 = 16

16 × 5.0625 = 81

so, it is neither.

f(x) = x⁴

this is actuality called a polynomial (of the 4th degree).

FYI : as we can also see, a linear function is also a polynomial (of the 1st degree).

User QuantumRich
by
7.9k points

Related questions

asked Nov 11, 2018 49.4k views
Teleaziz asked Nov 11, 2018
by Teleaziz
8.2k points
2 answers
2 votes
49.4k views
asked Nov 4, 2018 223k views
Knowads asked Nov 4, 2018
by Knowads
8.4k points
2 answers
5 votes
223k views