MATHEMATICS HIGH SCHOOL

The graph of y=√x is shifted 2 units up and 5 units left, Which equation represents the new graph?A. y=-√x+5) +2

B. y=-√x-2) +5

C. y=-√x+2) -5

D. y=-√x-5) +2

Answers

Answer 1

Answer:

y = √(x + 5) + 2

Further explanation

Given:

The graph of $y = √(x)$ is

shifted 2 units up, and
5 units left.

Question:

Which equation represents the new graph?

The Process:

The translation is a form of transformation geometry.

Translation (or shifting): moving a graph on an analytic plane without changing its shape.

In general, given the graph of y = f(x) and v > 0, we obtain the graph of:

$\boxed{ \ y = f(x) + v \ }$ by shifting the graph of $\boxed{ \ y = f(x) \ }$ upward v units.
$\boxed{ \ y = f(x) - v \ }$ by shifting the graph of $\boxed{ \ y = f(x) \ }$ downward v units.

That's the vertical shift, nowthe horizontal one. Given the graph of y = f(x) and h > 0, we obtain the graph of:

$\boxed{ \ y = f(x + h) \ }$ by shifting the graph of $\boxed{ \ y = f(x) \ }$ to the left h units.
$\boxed{ \ y = f(x - h) \ }$ by shifting the graph of $\boxed{ \ y = f(x) \ }$ to the right h units.

Therefore, the combination of vertical and horizontal shifts is as follows:

$\boxed{\boxed{ \ y = f(x \pm h) \pm v \ }}$

The plus or minus sign follows the direction of the shift, i.e., up-down or left-right.

- - - - - - - - - -

Let's solve the problem.

Initially, the graph of $y = √(x)$ is shifted 2 units up.

$\boxed{y = √(x) \rightarrow is \ shifted \ 2 \ units \ up \rightarrow \boxed{ \ y = √(x) + 2 \ }}$

Followed by shifting 5 units left.

$\boxed{y = √(x) + 2 \rightarrow is \ shifted \ 5 \ units \ left \rightarrow \boxed{ \ y = √(x + 5) + 2 \ }}$

Thus, the equation that represents the new graph is $\boxed{\boxed{ \ y = √(x + 5) + 2 \ }}$

The answer is A.

Learn more

Which phrase best describes the translation from the graph y = 2(x – 15)² + 3 to the graph of y = 2(x – 11)² + 3? brainly.com/question/1369568
The similar problem of shifting brainly.com/question/2488474
What transformations change the graph of (f)x to the graph of g(x)? brainly.com/question/2415963

Keywords: the graph of, y = √x, shifted 2 units up, 5 units left, which, the equation, represents, the new graph, horizontal, vertical, transformation geometry, translation

Answer 2

Answer:

Answer:

A. $y=√(x+5)+2$ .

Step-by-step explanation:

We are given the function $y=√(x)$ .

Now, the function is shifted 2 units up and 5 units to the left.

That is, the function is translated 2 units up and 5 units to the left.

Since, we know,

Translation of 'k' units up changes the function $f(x)$ to $f(x)+k$ .

So, the function translated 2 units up is $y=√(x)+2$ .

Translation of 'k' units to the left changes the function $f(x)$ to $f(x+k)$ .

So, the new function translated 5 units left is $y=√(x+5)+2$ .

Hence, the equation representing the new function is $y=√(x+5)+2$ .

Related Questions

In the following series of numbers, please identify the lowest number? 1.7 7 0.7 0.37 17
if we have a geometric series with u1 = 2.1 and r= 1.06, what would the least value of n be such that Sn > 5543?
Luke takes a sheet of paper and cuts from one corner to the opposite corner, making two triangles. If the piece of paper is 16 inches long and 12 inches wide, how long is the dagonal cut that Luke made? Make sure to show your work and explain ypur answer.
A regular hexagon has perimeter 60 in. What is the hexagon's area?
Form a union for the following sets. K = {2, 3, 5, 8} L = {3, 5, 7} a. { } b. {3, 5} c. {2, 3, 5, 7, 8} d. {2, 7, 8}

What is the solution to the equation?5=2/5a

A.2

B.4 3/5

C.12 1/2

D.25

Answers

Answer:

Exact form - $(25)/(2)$

Decimal form - 12.5

Mixed number form - 12 $(1)/(2)$

Have a nice day.

Lebron James shot the ball 1103 times during the 2019-2020 basketball season. He made 643 of the shots. What is his shooting percentage?

Answers

Answer:

1.71539657854

Step-by-step explanation:

After college start you start a job earning 38,000 a year. You get a 5% raise each year.A.) Write the first 3 terms of the sequence.
B.) How much will you earn over a 40 year period?
Show all work

Answers

Hi

38000+5%=39900

So 40x5=200
39900+200%=119700

so if he works there for 40yrs he would earn $119700 a yr

119700/12=1641.66667per month

Braeden has an income of $85,600 before income tax.The income tax rate is 3.5%. How much will he pay in
income taxes?

Answers

9514 1404 393

Answer:

$2996

Step-by-step explanation:

3.5% of $85,600 is ...

0.035 × $85,600 = $2996

Braeden will pay $2,996 in income taxes.

(-6x+3)-(-6x+8)
jrye ga ue,j

Answers

Answer:

(-6x + 3) - (-6x + 8) simplifies to 11.

Use the given information to find the equation of the quadratic function. Write the equation in standard form f(x) = ax2 + bx + c. The zeros of the function are x = 2 and x = −5, and there is no constant multiplier.