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oksian1 [2.3K]
3 years ago
9

Geraldine is asked to explain the limits on the range of an exponential equation using the function f(x) = 2^x. She makes these

two statements:

Mathematics
2 answers:
GalinKa [24]3 years ago
8 0

<u>General Idea:</u>

Domain is the values of x which gives a defined output to the function, and Range is the values of y that we get by substituting domain values of x. For the function f(x) = a^x, where a > 0, the domain will be all real numbers and range will be all values greater than 0. That is the graph will be very close to x-axis but will never touch it.

<u>Applying the concept:</u>

From the attached table, we can notice that as x increases infinitely, the y-values are continually doubled for each single increase in x and as x decreases infinitely, the y-values are continually halved for each single decrease in x.

Option 1: "Statement 1 is incorrect because the y-values are increased by 2, not doubled".

Option 1 is INCORRECT because Statement 1 is TRUE & CORRECT.

Option 2: "Statement 2 is incorrect because the y-values are doubled, not halved".

Option 2 is INCORRECT because Statement 2 is TRUE & CORRECT.

Option 3: "The conclusion is incorrect because the range is limited to the set of the integers"

Option 3 is INCORRECT because, the range will be always greater than 0, because irrespective of how many times y is halved for each single decrease in x, the y will still be a positive fraction and won't be a negative.

Option 4: "The conclusion is incorrect because the range is limited to the set of positive real numbers"

<em><u>Option 4 is CORRECT because y value will be positive irrespective of whatever x we substitute in the function.</u></em>

Inga [223]3 years ago
4 0

Answer:

Option 4 is the Correct answer!

Hope I helped! :}

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Answer:

−a^2 b^2 + 2a + 2b

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Step-by-step explanation:

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8 0
2 years ago
Identify the slope and y-intercept of a graph of the equation y=1/2x-5
ehidna [41]

Answer:

Slope: 1/2

y-intercept: -5

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7 0
3 years ago
Which equation represents a line passing through the point (8,33) with a slope of 3?
Delvig [45]

The slope intercept form of equation of required line is y = 3x + 9

What is equation of line in slope intercept form?

The most general form of equation of line in slope intercept form is given by y = mx + c

Where m is the slope of the line and c is the y intercept of the line.

Slope of a line is the tangent of the angle that the line makes with the positive direction of x axis.

If  \theta is the angle that the line makes with the positive direction of x axis, then slope (m) is given by

m =  tan\theta

The distance from the origin to the point where the line cuts the x axis is the x intercept of the line.

The distance from the origin to the point where the line cuts the y axis is the y intercept of the line.

Here,

Slope = 3

The line passes through (8, 33)

Equation of required line

y - 33 = 3(x - 8)

y - 33 = 3x - 24

y = 3x - 24 + 33

y = 3x + 9

To learn more about equation of line in slope intercept form, refer to the link:

brainly.com/question/25514153

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6 0
1 year ago
If 2= (1+ r)^7 solve the equation for r?​
solong [7]

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8 0
3 years ago
The average summer vacation costs $2252. If 82% of this amount is charged on credit cards, then what amount of the vacation cost
expeople1 [14]

Answer: $1846.64

Step-by-step explanation:

Given : The average summer vacation costs $2252.

If 82% of this amount is charged on credit cards, then the amount of the vacation cost is charged will be :-

82\%\text{ of }\$2252\\\\\text{Convert percent into fraction by dividing it by 100, we get}\\\\=\$[\dfrac{82}{100}\times2252]\\\\=\$[\dfrac{184664}{100}]\\\\=\$1846.64

Therefore the amount of the vacation cost is charged= $1846.64

3 0
2 years ago
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