Amia has $300 to plan a trip with her cousins. She wants to go to Orlando, Florida and it costs $127 for a room, $75 for gas rou
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Function transformation involves changing the form of a function
The function g(x) is
The function is given as:
g(x) is an exponential function that passes through points (-2,2) and (-1,4).
An exponential function is represented as:
At point (-2,2), we have:
At point (-1,4), we have:
Divide both equations
Simplify
Apply law of indices
Rewrite as:
Substitute 2 for b in
This gives
Multiply both sides by 4
Substitute 8 for (a) and 2 for (b) in
Express as a function
Hence, the function g(x) is
Read more about exponential functions at:
Answer:
The first choice, .
Step-by-step explanation:
The dashed vertical line is a vertical asymptote. The x-coordinate of all points on this vertical asymptote are equal to 7. In other words, when the x-value of a point on the graph approaches , its y-value approaches infinity (or negative infinity.)
Either way, the graph is not defined for . The point
should thus be excluded from the domain of the graph.
The graph is apparently defined for all other x-values. The domain of the function should thus be all real numbers with the exception of . Here's how to write that in interval notation:
- The set of all real numbers can be expressed as the interval
. Note that infinity
(or
itself isn't a real number. The round brackets indicate that both endpoints are excluded from the from the interval.
- The set of all real numbers less than (not equal to)
is
(both ends are excluded.) The set of all real numbers greater than (not equal to)
.
- The set of all real numbers that is not equal to
connects two intervals.
In other words, the domain is .