Question

select which function has the greatest value at each of the given x-values.
$f(x)=2x + 4$
$g(x)=x^{2}+2x - 1$
$h(x)=5^{(x-3)}$
$x=0$
$x=2$
$x=4$
$x=6$
$x=8$

Explanation:

Step1: Calcular $f(x), g(x), h(x)$ para $x=0$

$f(0)=2(0)+4=4$
$g(0)=0^2+2(0)-1=-1$
$h(x)=5^{(0-3)}=\frac{1}{5^3}=\frac{1}{125}=0.008$
Mayor valor: $f(x)$

Step2: Calcular $f(x), g(x), h(x)$ para $x=2$

$f(2)=2(2)+4=8$
$g(2)=2^2+2(2)-1=4+4-1=7$
$h(x)=5^{(2-3)}=\frac{1}{5^1}=0.2$
Mayor valor: $f(x)$

Step3: Calcular $f(x), g(x), h(x)$ para $x=4$

$f(4)=2(4)+4=12$
$g(4)=4^2+2(4)-1=16+8-1=23$
$h(x)=5^{(4-3)}=5^1=5$
Mayor valor: $g(x)$

Step4: Calcular $f(x), g(x), h(x)$ para $x=6$

$f(6)=2(6)+4=16$
$g(6)=6^2+2(6)-1=36+12-1=47$
$h(x)=5^{(6-3)}=5^3=125$
Mayor valor: $h(x)$

Step5: Calcular $f(x), g(x), h(x)$ para $x=8$

$f(8)=2(8)+4=20$
$g(8)=8^2+2(8)-1=64+16-1=79$
$h(x)=5^{(8-3)}=5^5=3125$
Mayor valor: $h(x)$

Answer:

• Para $x=0$: Marcar la casilla de $f(x)=2x+4$
• Para $x=2$: Marcar la casilla de $f(x)=2x+4$
• Para $x=4$: Marcar la casilla de $g(x)=x^2+2x-1$
• Para $x=6$: Marcar la casilla de $h(x)=5^{(x-3)}$
• Para $x=8$: Marcar la casilla de $h(x)=5^{(x-3)}$