Original function:
[tex]f(x)=2^x[/tex]
The transformed function has a reflection over the x-axis and a shift downward, as in our function, the y-intercept (when we set the x to 0 in the equation) is at (0,1).
Then, to make a reflection about the x-axis we have to add a minus sign:
[tex]f(x)=-2^x[/tex]
Finally, to get the y-intercept at (0, -3), we have to subtract two to our function:
[tex]f(x)=-2^x-2[/tex]
Proving that it is correct:
[tex]f(0)=-2^0-2=-1-2=-3[/tex]
Answer:
[tex]f(x)=-2^x-2[/tex]
• Coefficient: -2
,
• Exponent: ,x
,
• Constant: -2
