If the parent function is y=1/x describe the change in the equation y=5/x

Question

None of the other answers are correct

Moves 5 units to the left

Moves 5 units up

Vertical stretch by a factor of |5|

Moves five units to the right

Answer 1

Because ⁵/_x = 5 (¹/_x) = 5y for y = ¹/_x, this is a vertical stretch by a factor of 5.

A vertical stretch by a factor of 5 means with the same "input" or x-value, the "output" or y-value will be multiplied by 5.

So when f(x) = 1/x g(x) = 5/x

f(1) = 1/1 = 1 g(1) = 5/1 = 5 ;vertical stretch by factor of 5

f(2) = 1/2 g(2) = 5/2 ;vertical stretch by factor of 5

f(5) = 1/5 g(5) = 5/5 = 1 ;vertical stretch by factor of 5

Answer 2

The difference in the equations y=1/x and y=5/x is that the second equation has been multiplied by 5.

In the function y=a/(x-b)+c, the graph will be moved up c and to the right b units, and vertically stretched by a factor of a, compared to y=1/x.

If you ever forget that, like on a test, just plot a few points, or just make a quick table and compare some values.

y=1/x y=5/x

x y x y

-2 -0.5 -2 -2.5

-1 -1 -1 -5

0 n/a 0 n/a

1 1 1 5

2 2 2 2.5

I see a pattern that works for all five points, and that's that the outputs are five times the distance from zero.

Let me know if this needs any further explanation!

Answer 3

y=5/x is the same generally shaped curve, but every y value is 5 times as large as for the curve y=1/x

in the 1st quadrant or 5 times as small in the 3rd quadrant.

Both curves are hyperbolas, with each half of the hyperbola symmetric about the origin or the line y=-x

Both are asymptotic to the y and x axes.

but y=1/x approaches each axis faster than y=5/x

Both are standard hyperbolas rotated 45 degrees.

The vertices of the hyperbola y=1/x are (1,1) and (-1,-1) The vertices of y=5/x are

(5^1/2, 5^1/2) and (-5^1/2, -5^1/2). The vertices are the two points that are the shortest

distance from one half of the hyperbola to the other half. Halfway between the

vertices, on either y=1/x or y=5/x is the origin (0,0)

To go from a point on the graph of y=1/x to the corresponding point on y=5/x is

equivalent to stretching y values by a factor of the absolute value of 5

or moving the curve left by a factor of 5 in quadrant 3

or downward by a factor of 5

and moving the curve right by a factor of 5 in quadrant 1

or upward by a factor of 5

If you want to move from y=1/x to y=5/x by moving 45 degrees along the

diagonal, move simultaneously upward and to the right, by a factor of

the square root of 5, in the 1st quadrant,

or move 45 degrees downward and to the left, by a factor of the

square root of 5 in quadrant 3. The point (1,1) shifted up to the right

becomes (5^1/2, 5^1/2) in quadrant 1, going from y=1/x to y=5/x

Neither curve has any y or x intercepts

The slopes of both curves approach the limit of zero as x approaches infinity

and negative or positive infinity as x approaches zero from left or right

For example if (2, 1/2) is a point on y=1/x then (10, 1/2) is a point on y=5/x

10 is 2 x 5. Multiply the x coordinate by 5 to get the corresponding point on y=5/x

Or if (2, 1/2) is on y=1/x then (2,5/2) is on y=5/x. Multiply the y coordinate by 5.

All x and y coordinates are symmetric. If (2,1/2) is on the graph, so is (1/2,2)

In general, if (x,y) is on the graph, so is (y,x) on the same graph. If (x,y) is on the graph of y=1/x then

so is (5x,y) and (x,5y) on the graph of y=5/x. That's the shift up or to the right by factor of 5.

Unless x and y are negative, then the shift is down or to the left by a factor of 5

The hyperbola is a conic section, a vertical slice of two cones, joined together at their pointed bottom,

one cup right side up and one upside down, shaped

like some paper cups at the water cooler.

The hyperbola is the only conic section that has two separate disjoint halves. Each half is in

a different quadrant

Answer 4

Because ⁵/_x = 5 (¹/_x) = 5y for y = ¹/_x, this is a vertical stretch by a factor of 5.