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$\text { If } f(x)=3 x^{2}-x+2, \text { Find } f(2), f(-2), f(a), f(-a)$

$f(x)=3 x^{2}-x+2$

$f(2)=3(2)^{2}-2+2=12$

$f(-2)=3(-2)^{2}-(-2)+2=12+2+2=16$

$f(a)=3(a)^{2}-a+2=3 a^{2}-a+2$

$f(-a)=3(-a)^{2}-(-a)+2=3 a^{2}+a+2$

$\text { The graph of a function } f \text { is given. }$

(a) State the value of $f(1)$
(b) Estimate the value of $f(-1)$

(c) For what values of $x$ is $f(x)=1 ?$
(d) Estimate the value of $x$ such that $f(x)=0$

(e) State the domain and range of $f$
(f) On what interval is $f$ increasing?

$(a) f(1)=3$

$\text { (b) } f(-1)=-0.4$

$\text { (c) } f(x)=1 \quad x=?$

$x=0 \quad f(0)=1$

$(d) \quad f(x)=0 \quad x=?$

$f(-0.6)=0$

$\text { (e) Domain }[-2,4]$

$\text { Ronge }[-1,3]$

$(-2,1)$

Find the domain of the function $F(x)=\frac{x+4}{x^{2}-9}$

$x^{2}-9=0 \quad \longrightarrow(x+3)(x-3)=0$

$x=\pm 3$

$D : R / \pm 3$

$D :(-\infty,-3) \cup(-3,3) \cup(3, \infty)$

Find the domain of the function $f(x)=\frac{2 x^{3}-5}{x^{2}+x-6}$

$+x^{2}+x-6=0 \longrightarrow(x+3)(x-2)=0$

$x=-3$
$x=2$

$D :(-\infty,-3) \cup(-3,2) \cup(2,-\infty)$

Find the domain and sketch the graph of the function $f(x)=1.6 x-2.4$

$f(x)=1.6 x-2.4$

$a x+b$

Domain : R

$f(0)=1.6(0)-2 \cdot 4=-2.4 \quad(0,-2.4)$

$f(1)=1.6(1)-2.4=-0.8 \quad(1,-0.8)$