Answer:
a graph can be divided into 4 quadrants.
a zero abscissa, means the point lies on the origin.
a negative ordinate means the point lies on the y axis in the third and fourth quadrants.
Remember the basic trig identity
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We can move the cosine term to the right side to get
We can then replace
in the original equation and basically factor the resulting equation like a quadratic:
Then, we can see that
either equals
or
. But since the range of cosine is only from
, cosine can't equal
at all! So, you just have to solve for x when
, which is when
(The last part of the solution says that k can be any integer.)
If you only want solutions in the range
, then your answer is just
If k>0, then the graph of the function g(x) = (0.5)x − k is obtained from the graph of the function <span>f(x) = (0.5)x by translation k units down.
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<span>Since g(x) is obtained by shifting f(x) down by 3 units, the value of k is 3.
</span><span>
</span><span>Answer: k=3.</span>