Find g(3) show all steps g(3) = 2x + 4
2 answers:
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The red graph is the result of a vertical translation, 4 units down, of the black graph.
This means that, whenever the black graph associates
The red graph must associate 4 less to the same input:
So, the equation for the red graph is
or, equivalently,
A reflection about the x axis, about y=0, is the mapping (x',y')=(x,-y) so
A dilation of 2 is the mapping (x'',y'')=(2x', 2y')
So
We can rewrite that without the primes and combine the powers of 2.
Let's graph these and see if we're close,
Plot y= (1/4)^x, y= - (1/4)^{x}, y = - 2^{1-x}
