the complete question in the attached figure
using a graphical tool ---------------- > see attached figures
1 f(1) is less than g(−1)
we have that
f(1)=-33 and g(-1)=20(1.5)^(-1)=20*(1/1.5)=13.33-------- > g(x) is not negative
therefore
f(1) is less than g(−1)---------------- > true
2. f(x) increases at a faster rate than g(x) does on the interval (−5, −3) .
g(-5)=2.634 g(-3)=5.926 (5.926/2.634)=2.25
2.25-1=1.25--------------- >the rate increases at 125%
f(-5)=-45 f(-3)=-49 49/45=1.09
1.09-1=0.09--------------- >the rate increases at 9%
in the interval (−5, −3) g(x) increases at a faster rate than f(x)
therefore
f(x) increases at a faster rate than g(x) does on the interval (−5, −3)---> false
3. g(x) has a greater y-intercept than f(x) does
g(x) y-intercept----------- > is 20
f(x) y-intercept----------- > is -40
20>-40
therefore
g(x) has a greater y-intercept than f(x) does--------------> true
4. f(x) and g(x) are both increasing on the interval (−∞, ∞)------> true
the answers are
f(1) is less than g(−1)
g(x) has a greater y-intercept than f(x) does
f(x) and g(x) are both increasing on the interval (−∞, ∞)
