1 Let f(r) = (r – 1)², g(x) = 1– a², h(x) = 2(r + 3)2 – 8, find for each functiona) r- and y- intercepts.b) vertexc) graph

Answered: 1 Let f(r) = (r – 1)?, g(x) = 1– r²,…

1 Let f(r) = (r – 1)?, g(x) = 1– r², h(r) = 2(x+ 3)2 – 8, find for each function a) r- and y- intercepts. b) vertex c) graph

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter3: Functions And Graphs

Section3.5: Graphs Of Functions

Problem 59E

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Concept explainers

Domain

In simple mathematics terms, a domain is defined as the space on which all the possible inputs for the function will lie. It can also be expressed as a set of departures for the required function.

Question

1 Let f(r) = (r – 1)², g(x) = 1– a², h(x) = 2(r + 3)2 – 8, find for each function
a) r- and y- intercepts.
b) vertex
c) graph

Expert Solution

Step 1

Given :

$f (x) = {(x - 1)}^{2} g (x) = 1 - x^{2} h (x) = 2 {(x + 3)}^{2} - 8$

Step 2

We have to find x-and y- intercepts,vertex and draw the graph.

1) $f (x) = {(x - 1)}^{2}$

a) x- and y- intercepts

$y = f (x) = {(x - 1)}^{2} P u t x = 0 y = {(0 - 1)}^{2} y = 1 T h e r e f o r e x - i n t e r c e p t i s (0, 1) P u t y = 0 {(x - 1)}^{2} = 0 x - 1 = 0 x = 1 T h e r e f o r e y - i n t e r c e p t i s (1, 0)$

b) vertex

$The vertex is the average of the zeros . y = {ax}^{2} + bx + c x = - \frac{b}{2 a} y = x^{2} - 2 x + 1 x = - \frac{(- 2)}{2 \cdot 1} = \frac{2}{2} = 1 put x = 1 in above equation y = {(1)}^{2} - 2 (1) + 1 = 1 - 2 + 1 = 0 y = 0 vertex is (1, 0)$

c) graph

The graph of $f (x) = {(x - 1)}^{2}$ is

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