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Find the y-intercept of each exponential function and order the functions from least to greatest y-intercept. ?

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1 Answer
Jun 19, 2018

Answer:

Tile 1 - Tile 3 - Tile 2

or

Tile 3 - Tile 1 - Tile 2

Explanation:

Tile One:

The #y#-intercept is #-1# as shown in the graph.

Tile Two:

The coordinates of a #y#-intercept always has its #x#-coordinate as #0#. i.e. #(0, y)#

Thus, in the table, the #y#-intercept can be found by finding the value of #y# (which is equivalent to #f(x)# ) when #x = 0# which is #f(x) = 2#.

Tile Three:

If we put the explanation into a function, it would become:

#g(x) = a\times2^x# where a is an unknown constant.

If we inserted the coordinates into the function that we've created, we get:

#-2 = 2a#

#\therefore a = -1#

and now, we can complete the function to get:

#g(x) = -2^x#

To find the #y#-intercept, we have the #x#-coordinates as #0#:

#g(0) = -2^0#

#g(0) = -1#

#\thereforey#-intercept is #-1#.

Final answer:

Now we can just arrange the tiles in order of the values of the #y#-intercept.

Thus, the order is:

Tile 1 - Tile 3 - Tile 2

or

Tile 3 - Tile 1 - Tile 2

Hope that makes sense!