What is the difference between y=sqrtx +3 and y=2sqrtx +3
(I put spaces between x and the + to show that only the x is a squareroot)
And what is the difference between y=2sqrtx +3 and y=sqrt2x+3
When I mean the difference, I mean how they would look differently when graphed.
Thanks in advance!
one is shifted upward slightly, but they have the same shape.
y=2sqrtx +3 will be slightly shifted upward compared to y=sqrtx +3?
To understand the difference between the given equations and how they would look differently when graphed, let's break them down:
1. y = √x + 3
2. y = 2√x + 3
3. y = √(2x) + 3
1. The equation y = √x + 3 represents a square root function. This means that for each value of x, you take the square root of x and then add 3 to it. This equation will produce a curved graph that starts from the point (0, 3) and rises as x increases.
2. The equation y = 2√x + 3 is similar to the first equation but with a key difference: the coefficient in front of the square root is 2. This means that each value of x will be multiplied by 2 before taking the square root. As a result, the graph of this equation will be steeper than the first equation. It will also start from the point (0, 3) but rise more quickly.
3. The equation y = √(2x) + 3 combines the features of the previous two equations by both squaring the x-value and then multiplying it by 2. As a result, this equation will produce a graph that starts from (0, 3) and rises more steeply than the first equation but less steeply than the second equation.
In summary, when graphed, the three equations will have the same shape of a curved increase, represented by a square root function. However, their graphs will differ in terms of the steepness of the incline. The graph of y = √(2x) + 3 will be steeper than that of y = √x + 3, and the graph of y = 2√x + 3 will be steeper than both.