All categories

2 years ago

Function g can be thought of as a translated (shifted) version of f(x)=x^2

Mathematics

2 answers:

Andrei [34K]2 years ago

4 0

Answer: g(x) = (x+2)^2+1

zalisa [80]2 years ago

3 0

Given:

The parent function is $f(x)=x^2$

We need to determine the equation for the new function g(x)

Vertical shift:

From the graph, it is obvious that the parent function is shifted 6 units upwards.

The general rule to shift the graph c units upwards is $f(x)+c$

Thus, using the rule, the vertical shift of the new function g(x) is given by

$g(x)=x^2+6$

Horizontal shift:

From the graph, it is obvious that the parent function is shifted 2 units to the right.

The general rule to shift the graph c units to the right is $f(x-c)$

Thus, the horizontal shift of the new function g(x) is given by

$g(x)=(x-2)^2$

Equation for the new function g(x):

Since, the new function is shifted 2 units to the right and 6 units upward is given by the equation,

$g(x)=(x-2)^2+6$

Hence, the equation of the new function is $g(x)=(x-2)^2+6$

You might be interested in

Solve for z a(t+z)=45z+67

ladessa [460]

Solve for z a(t+z)=45z+67
1. Expand
$at+az=45z+67$

2. Subtract $at$ from both sides
$az=45z+67-at$

3. Subtract 45z from both sides
$az-45z=67-at$

4. Factor out the common term z
$z(a-45)=67-at$

5. Divide both sides by a - 45
$z= \frac{67-at}{ya-45}$

Answer: $z= \frac{67-at}{a-45}$

6 0

2 years ago

Read 2 more answers

Is 14 quarter inches the most common measurement

borishaifa [10]

^ if you're talking universally, no it would be cm. But no one really says "quarter inches". You would just say inches

7 0

2 years ago

Which of the following describes the graph of y = StartRoot negative 4 x minus 36 EndRoot compared to the parent square root fun

RoseWind [281]

Answer:

stretched by a factor of 2, reflected over the y-axis, and translated 9 units left

Step-by-step explanation:

The given function is $y=\sqrt{-4x-36}$

We can rewrite this function by factoring -4 in the radicand to get:

$y=\sqrt{-4(x+9)}$

We further simplify the square root of 4 to get:

$y=2\sqrt{-(x+9)$

The parent function is $y=\sqrt{x}$

When we compare to the parent function, there is a stretch by a factor of 2, reflection over the y-axis, and translation 9 units left

The last option is correct

3 0

2 years ago

Read 2 more answers

A group of 18 people ordered soup and sandwiches for lunch. Each person in the group had either one soup or one sandwich. The sa

sergeinik [125]

X - the number of sandwiches ordered
y - the number of soups ordered

There were 18 people, and each person ordered either one soup or one sandwich.
$x+y=18$

The sandwiches cost $7.75 each, the soups cost $4.50 each. The total cost was $113.50.
$7.75x+4.5y=113.5$

Set up a system of equations:
$x+y=18 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ |\times (-4.5) \\
7.75x+4.5y=113.5 \\ \\
-4.5x-4.5y=-81 \\
\underline{7.75x+4.5y=113.5} \\
3.25x=32.5 \\
x=\frac{32.5}{3.25} \\
x=10$

10 sandwiches were ordered.
The answer is D.

4 0

2 years ago

Dave’s Automatic Door, referred to in Exercise 29, installs automatic garage door openers. Based on a sample, following are the

HACTEHA [7]

The question is not complete and the full question says;

Calculate the (a) range, (b) arithmetic mean, (c) mean deviation, and (d) interpret the values. Dave’s Automatic Door installs automatic garage door openers. The following list indicates the number of minutes needed to install a sample of 10 door openers: 28, 32, 24, 46, 44, 40, 54, 38, 32, and 42.

Answer:

A) Range = 30 minutes

B) Mean = 38

C) Mean Deviation = 7.2

D) This is well written in the explanation.

Step-by-step explanation:

A) In statistics, Range = Largest value - Smallest value. From the question, the highest time is 54 minutes while the smallest time is 24 minutes.

Thus; Range = 54 - 24 = 30 minutes

B) In statistics,

Mean = Σx/n

Where n is the number of times occurring and Σx is the sum of all the times occurring

Thus,

Σx = 28 + 32 + 24 + 46 + 44 + 40 + 54 + 38 + 32 + 42 = 380

n = 10

Thus, Mean(x') = 380/10 = 38

C) Mean deviation is given as;

M.D = [Σ(x-x')]/n

Thus, Σ(x-x') = (28-38) + (32-38) + (24-38) + (46-38) + (44-38) + (40-38) + (54-38) + (38-38) + (32-38) + (42-38) = 72

So, M.D = 72/10 = 7.2

D) The range of the times is 30 minutes.

The average time required to open one door is 38 minutes.

The number of minutes the time deviates on average from the mean of 38 minutes is 7.2 minutes

4 0

2 years ago