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

Then teach the underlying concepts
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Jun 19, 2018

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. $\left(0 , y\right)$

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

Tile Three:

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

$g \left(x\right) = a \setminus \times {2}^{x}$ where a is an unknown constant.

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

$- 2 = 2 a$

$\setminus \therefore a = - 1$

and now, we can complete the function to get:

$g \left(x\right) = - {2}^{x}$

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

$g \left(0\right) = - {2}^{0}$

$g \left(0\right) = - 1$

$\setminus \therefore y$-intercept is $- 1$.

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!

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