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san4es73 [151]
3 years ago
8

How to graph exponential function y=6^x-4

Mathematics
1 answer:
sladkih [1.3K]3 years ago
7 0
That is an exponential function. It grows all over the range, from - ∞ to + ∞.

The limit when f(x) goes of - ∞ is zero, so y = 0 there is the asymptote to the left side.

The value of f(x) for x = 4 is 1: f(4) = 6 ^ (4 - x) = 6 ^ (4 - 4) = 6^0 = 1. So, the y intercept is y = 0.

The function grows as x goes to infinity.

You can finds some other values of the function to help to sketch the graph.

x             f(x) = 6 ^ (x - 4)

-100      6^ ( -104) = 1.18 * 10^ (-81)

- 10       6^ (-14) = 1.28 - 10^ -11

3           6^ (-1) = 1/6 = 0.17

4           6^0 = 1

14         6^ (10) = 60,466,176
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The coordinate of the vertex is; (h, k) = (3, -5)

The final equation of the parabola is; y = 5(x - 3)² - 5

<h3>How to find the vertex of a Parabola?</h3>

The vertex is the coordinate of the crest or trough of the curve. Now, in the given graph, we only have a Trough which is the lowest point of the graph.

The coordinate of the vertex is; (h, k) = (3, -5)

2) Since the general equation is;

y = a(x - h)² + k

We will have;

y = a(x - 3)² - 5

At x = 2, y = 0. Thus;

0 = a(2 - 3)² - 5

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3) The final equation of the parabola is;

y = 5(x - 3)² - 5

Read more about Parabola Vertex at; brainly.com/question/17987697

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The scale of a room in blueprint is 3in 5ft. A wall in the same blueprint is 18in. what are the actual room measurements?
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Answer:

Actual length of wall = 30ft

Step-by-step explanation:

We have scale of a room as 3 inch for 5ft.

We can write scaling factor as:

Scaling factor = 3 /60     (Since 5ft = 60 inches )

Scaling factor = 1/20

Now,

a wall in the blueprint is 18inch.

So actual length of wall can be determined by dividing 18 inch by the scale factor.

i.e actual length of wall = 18 / scale factor  = 18 / (1/20)

 actual length of wall = 18* 20 = 360 inch = 30ft (Since 360 inch = 30ft)

Hence Actual length of wall = 30ft

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3 years ago
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