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3 years ago

Match the function with its graph.

Mathematics

1 answer:

Oxana [17]3 years ago

4 0

Answer:

The answer is 1D , 2A , 3C , 4B ⇒ answer (c)

Step-by-step explanation:

* Lets talk about the transformation

- If the function f(x) reflected across the x-axis, then the new

function g(x) = - f(x)

- If the function f(x) translated horizontally to the right

by h units, then the new function g(x) = f(x - h)

- If the function f(x) translated horizontally to the left

by h units, then the new function g(x) = f(x + h)

* Lets explain each function

∵ y = tan(x)

∵ y = -tan(x - π/2)

# (x - π/2) means the graph translated horizontally to

the right π/2 units

# -tan(x - π/2) means the graph reflected across the x-axis

∴ The graph is (D)

* 1) y = -tan(x - π/2) ⇒ (D)

∵ y = tan(x + π/2)

# (x + π/2) means the graph translated horizontally to

the left π/2 units

∴ The graph is (A)

* 2) y = -tan(x - π/2) ⇒ (A)

∵ y = -cot(x - π/2)

# (x - π/2) means the graph translated horizontally to

the right π/2 units

# -cot(x - π/2) means the graph reflected across the x-axis

∴ The graph is (C)

* 3) y = -cot(x - π/2) ⇒ (C)

∵ y = cot(x + π/2)

# (x + π/2) means the graph translated horizontally to

the left π/2 units

∴ The graph is (B)

* 4) y = -tan(x - π/2) ⇒ (B)

∴ The answer is 1D , 2A , 3C , 4B answer (c)

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Romashka-Z-Leto [24]

Answer:

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Step-by-step explanation:

A function is "increasing" when its graph goes up to the right, the slope is positive. At a turning point (maximum or minimum), the function is neither increasing nor decreasing.

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1 year ago

Ingrid makes quilts in designs that follow a specific pattern. The first three designs are shown. In designs, the white blocks r

Gekata [30.6K]

The number of white and grey blocks in the quilts follows a sequence given by the Design number of the quilt

The numbers and patterns of the blocks are;

a. Patterns;

The height of the white blocks is the Design number, while the rows are one more than the design number

The height of the outer grey blocks is 2 blocks more than the Design number, while their rows are 3 blocks more than the Design number

b. The function is $\underline{p(n) = n \cdot (n + 1)}$

c. The function is $\underline{b(n) = (n + 2) \cdot (n + 3) - n \cdot (n + 1)}}$

d. $\underline{t(n) = (n + 2) \cdot (n + 3) = b(n) - p(n) }$

e. The design chosen is Design 9

The number of blocks is 132 blocks

Reasons:

The pattern of the design are;

a. The column height of the grey blocks = 2 blocks more than the column height of the white blocks

Width of the outer grey blocks = 2 blocks more than the width of the inner white blocks

The number of white blocks in a design, n is the product of n and (n + 1)

The number of grey blocks in a design n, is the product of (n + 2) and (n + 3) less the number of white blocks in the design

b. Based on the above, the function that represent the number of picture blocks in Design n, is therefore;

p(n) = n·(n + 1)

c. Based on the above, the function that represent the number of border blocks in Design n, is therefore;

b(n) = (n + 2)·(n + 3) - n·(n + 1)

d. The total number of blocks, t(n) = (n + 2)·(n + 3)

t(n) = (n + 2)·(n + 3) - n·(n + 1) + n·(n + 1)

t(n) = p(n) + b(n)

e. The given number of picture blocks = 90

The number of picture blocks in a design, n = n × (n + 1)

Therefore, given that the number of picture blocks is 90, we have;

90 = n × (n + 1)

n² + n - 90 = 0

(n + 10)·(n - 9) = 0

n = 9, or n = -10

Therefore, the design museum chooses is Design 9

The total number of blocks in a quilt design, t(n) = (n + 2)·(n + 3)

Total blocks in the design the art museum choses, t(9), is given as follows;

t(9) = (9 + 2)·(9 + 3) = 132 blocks

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2 years ago

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Answer:

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Step-by-step explanation:

Well let's first graph the quadratic equation,

Look at the image below ↓

By looking at the image below we can tell that the graph touches the x axis 2 times at,

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Thus,

the parabola touches the x axis twice.

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2 years ago

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Answer:

Hey there!

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