Sketched below is the graph of $f(x) = k^x; k > 0$ - NSC Mathematics - Question 6 - 2019 - Paper 1
Question 6
Sketched below is the graph of $f(x) = k^x; k > 0$. The point $(4; 16)$ lies on $f$.
5.1 Determine the value of $k$.
5.2 Graph $g$ is obtained by reflecting graph ... show full transcript
Worked Solution & Example Answer:Sketched below is the graph of $f(x) = k^x; k > 0$ - NSC Mathematics - Question 6 - 2019 - Paper 1
Step 1
Determine the value of $k$
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Answer
To find the value of k, we use the point (4;16) which lies on the graph of f(x)=kx.
Substituting the coordinates into the function:
f(4)=k4=16.
Taking the fourth root of both sides gives:
k=161/4=2.
Thus, the value of k is 2.
Step 2
Determine the equation of graph $g$
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Answer
Reflecting the graph f about the line y=x helps us find the equation of graph g. The transformation related to the reflection implies that if y=kx, then for graph g, we express x in terms of y.
Starting from:
y=kxextbecomesx=ky.
Substituting k=2 gives:
x=2y.
In standard function form, the equation for graph g is:
y = rac{ ext{log}_2(x)}{}.
