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3 years ago

Which of the following is equal to g(x)?

Mathematics

1 answer:

sweet-ann [11.9K]3 years ago

3 0

Answer: Option D

$g(x) = 3 ^ x +1$

Step-by-step explanation:

If we have a function f(x), then the graph of $y = f (x)$ can be shifted upwards k units using the transformation $g (x) = f (x) + k$ .

Where k is a positive number.

In this problem the function f(x) is:

$f (x) = 3 ^ x$

This function has its intercept with the y-axis in y = 1

Then, the graph of g(x) is equal to the graph of f(x) shifted 1 unit up and cuts to the y axis in y = 2.

Therefore g(x) is equal to the function f(x) after the transformation $y = f(x) +1$

So:

$g(x) = 3 ^ x +1$

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What is the absolute value transformation of this function?

xxMikexx [17]

Answer:

k(x) = -|x + 2| + 3

Step-by-step explanation:

Parent function of the absolute function given in the graph,

f(x) = |x|

1). Function 'g' is reflected across the x-axis, then the image will be,

h(x) = -f(x) = -|x|

2). Function 'h' the shifted 2 units left and 3 units upwards, image function will be,

k(x) = h(x + 2) + 3

k(x) = -|x + 2| + 3

Therefore, the transformed function is k(x) = -|x + 2| + 3.

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3 years ago

00:57

prisoha [69]

<h3>Given:</h3>

h= 19 ft
r= 12 ft

h= Height
r= Radius

The volume of the given cone.

<h3>Solution:</h3>

$\large\boxed{Formula:V= \frac{1}{3}\pi{r}^{2}h}$

$\large\boxed{\red \pi \red = \red 3 \red . \red 1 \red 4}$

Let's solve!

Substitute the values according to the formula.

$V=\frac{1}{3}×3.14×{12}^{2}×19$

$\large\boxed{V=2863.68 \: {ft}^{3}}$

Therefore, the volume of the given cone is 2863.68 cubic feets.

5 0

2 years ago

What is the sign of 3x y3xy3, x, y when x>0x>0x, is greater than, 0 and y<0y<0y, is less than, 0?

jekas [21]

Answer:

$Negative$

Step-by-step explanation:

$We\ have\ to\ find\ sign\ of\ 3xy^3\\\\x>0\ and\ y0,y$

4 0

3 years ago

Read 2 more answers

olchik [2.2K]

The correct answer is: [B]: " 25 a²⁵ b²⁵ " .
_________________________________________________________
Explanation:
_________________________________________________________
Given the expression:
_________________________________________________________
→ " (−5a⁵b⁵)² (a³b³)⁵ " ; Simplify.
_________________________________________________________
Let us being by examining:
______________________________________
→ "(−5a⁵b⁵)² " .

→ "(−5a⁵b⁵)² = (-5)² * (a⁵)² * (b⁵)² = (-5)(-5) * a⁽⁵ˣ²⁾ * b⁽⁵ˣ²⁾ = 25a⁽¹⁰⁾b⁽¹⁰⁾ ;

{Note the following properties of exponents:
(xy)ⁿ = xⁿ * yⁿ ;

(xᵃ)ᵇ = x⁽ᵃ * ᵇ) ;

(xᵃ) * (xᵇ) = x⁽ᵃ ⁺ ᵇ⁾ .}.
______________________________________

Then, we examine:
______________________________________
→ "(a³b³)⁵ " .

→ "(a³b³)⁵ = a⁽³ˣ⁵⁾b⁽³ˣ⁵⁾ = a⁽¹⁵⁾b⁽¹⁵⁾ .
______________________________________

So: " (−5a⁵b⁵)² (a³b³)⁵ = (-5)a⁽¹⁰⁾b⁽¹⁰⁾ * a⁽¹⁵⁾b⁽¹⁵⁾ " ;
________________________________________
Now, we simplify:

→ " 25a⁽¹⁰⁾b⁽¹⁰⁾ * a⁽¹⁵⁾b⁽¹⁵⁾ " ;

→ " 25a⁽¹⁰⁾b⁽¹⁰⁾ * a⁽¹⁵⁾b⁽¹⁵⁾ ;

= 25a⁽¹⁰⁾ a⁽¹⁵⁾b⁽¹⁰⁾ b⁽¹⁵⁾ ;

= 25a⁽¹⁰ ⁺¹⁵⁾ b⁽¹⁰⁺¹⁵⁾ ;

= 25a⁽²⁵⁾ b⁽²⁵⁾ ;
_______________________________________________
→ which is: Answer choice: [B]: " 25 a²⁵ b²⁵ " .
______________________________________________

5 0

3 years ago

AABC~ ADEF. What is the scale factor? Help please

vladimir1956 [14]

Answer:

3:1 or 3

Step-by-step explanation:

the left triangle is scaling up to the right triangle. 5/15 is 1/3

7/21 is 1/3

4/14 is 1/3

since it is scaling UP, the scale factor is 3:1

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3 years ago