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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

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

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

 

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