- c.The graph off(x) = –^34
x
is always below
the x-axis and increases as xmoves from left to
right, as shown by its graph:
- d.The graph off(x) = –^175
3 x
is always below
the x-axis and is decreasing as xmoves from
left to right, as shown by its graph:
Set 49(Page 116)
- b.The graph off(x) = 1 – 2exis obtained by
reflecting the graph ofg(x) = exover the x-axis,
scaling it by a factor of 2, and then translating
it up one unit. In doing so, the original horizon-
tal asymptote y= 0 for gbecomes y= 1, and the
graph offalways stays below this asymptote.
Hence, the range is (–∞, 1). See the following
graph.
- c.Rewrite the expression on the right side of
the equation as a power of 2, as 4^3 x= (2^2 )^3 x=
26 x, and substitute into the original equation
to obtain the equivalent equation 2^7 x^2 –1= 2^6 x.
Now, equate the exponents and solve for x:
7 x^2 – 1 = 6x
7 x^2 – 6x– 1 = 0
(7x+ 1)(x– 1) = 0
The solutions are x= –^17 and x= 1.
- d.Since 215 = 5–2, the original equation is
equivalent to 5x+1= 5–2. The x-values that
satisfy this equation must satisfy the one
obtained by equating the exponents of the
expressions on both sides of the equation,
which is x+1= –2. But the left side of this
equation is nonnegative for any x-value that
does not make the radicand negative. Hence,
the equation has no solution.
–4–3–2–1 132
–2
–4
–6
–8
4
2
–10 –8 –6 –4 –2 2 4 6 8 10
–2
–4
–6
–8
–10
10
8
6
4
2
–10 –8 –6 –4 –2 2 4 6 8 10
–2
–4
–6
–8
–10
10
8
6
4
2
ANSWERS & EXPLANATIONS–
