How do u graph a function by translating its parent function?

Question

ex: y=2x+5

Answer 1

Its parent function is y=x.
Since the slope is 2, the line will be twice as steep (increasing).
The y value is increased by 5 for every x value, so shift the y = 2x graph up 5 units.

Answer 2

It's not clear from the wording of your question whether y=2x+5 is meant to be the parent function, or the translation, so I'll just discuss translations in general.

Given the graph of f(x), the graph of f(x+c), where c is positive, can be obtained by shifting the graph of f(x) by c units to the left. Similarly, the graph of f(x-c) can be obtained by shifting the graph of f(x) by c units to the right.

Also, the graph of f(x)+c can be obtained by shifting the graph of f(x) c units up, while the graph of f(x)-c can be obtained by shifting the graph of f(x) c units down.

Example: the graph of y=x^2+2x-2 can be obtained as follows: first, write it as y=(x+1)^2-3. Then, take the graph of x^2, shift it to the left by 1 unit, and down 3 units.

Answer 3

Assuming that this is the translated function and the parent function is y=x. then just streach the graph vertically by a factor of two (multiply all y coordinates on the graph by 2), then shift to the left five units (subtract 5 from each x coordinate)

Answer 4

find x and y intercepts by substituting o for y to find x, and likewise substituting o for x to find y,

0=2x+5

-5=2x

x=-5/2

y=2(0)+5

Plot either(not both of the x or y intercept)

so (0,5) or (5/2,0)

Say you plot (0,5) then y=m(x-xo) +y where m is slope, slope is always found in front of the x variable which in the case of theis linear equation, m=2,y=(2this is the slope)x+5

As such m=delta x/delta y or y2-y1/x2-x1 therefore m=rise over run

from either of the picked x or y coordinate begin to rise and run

m=2=2/1=rise/run=2 units rise then1 units run or the reciprocal by 2 units down and 1 unit left

therefore say you start at the coordinate (0,5),

you add rise of 2 to the x coordinate and run of 1 to the y coordinate
(-8.1)

(-6,2)

(-4,3)

(-2,4)
===========starting point and add -rise and -run according to x and y
(0,5)
===========starting point and add +rise and +run according to x and y

(2,6)

(4,7)

(6,8)

(8,9)




there now you have an image diagram slope of the linear equation on a cartesian place from the original equation

Answer 5

GET A GRAPHING CALCULATOR. it saved my existence. in case you have already got one, listed under are the stairs: pass to: Y= on the 1st area, variety contained in the be certain functionality: Y=X arrow down and contained in the 2d variety in: Y=(4^x)-3 press the GRAPH button. the 1st line to take place would be the y=x and the subsequent one would be the different equation desire i helped :)