/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Q. 10 g(x)聽= cos x(a) What is the y-i... [FREE SOLUTION] | 91影视

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Chapter 6: Q. 10 (page 408)

g(x)= cos x

(a) What is the y-intercept of the graph of g?

(b) For what numbers x, -蟺鈮�x鈮�蟺, is the graph of g

decreasing?

(c) What is the absolute minimum of g?

(d) For what numbers x,0鈮�x鈮�2蟺, does g(x)=0?

(e) For what numbers x, -2蟺鈮�x鈮�2蟺, does g(x) = 1?

Where does g(x) = -1?

(f) For what numbers x, -2蟺鈮�x鈮�2蟺, does g(x)=32?

(g) What are the x-intercepts of g ?

Short Answer

Expert verified

(a) The y-intercept is 1.

(b)

for decreasing function x鈭�0,蟺

(c) The absolute minimum of g is -1.

(d) g(x)=0forx鈭�{-3蟺2-蟺2,蟺2,3蟺2}

(e) g(x)=1forx=-2蟺,x=0andx=2蟺g(x)=-1forx=-蟺andx=蟺

(f) f(x)=32forx=-11蟺6,-蟺6,蟺6,11蟺6

(g) The x intercept is(2k+1)蟺2wherekisaninteger.

Step by step solution

01

Part (a) Step 1. Given Information

g(x)=cosx

02

Part (a) Step 2. Calculation

Since the graph of g(x)=cosx passes through (0,1) therefore the y-intercept of the graph is 1.

03

Part (b) Step 1. Calculation

The function g(x)=cosx is decreasing function fromx=0,蟺

04

Part (c) Step 1. Calculation

The amplitude of the g(x)=cosxis卤1 therefore the minimum value is -1.

05

Part (d) Step 1. Calculation

g(x)=0forx鈭�{-3蟺2-蟺2,蟺2,3蟺2}

06

Part (e) Step 1. Calculation

g(x)=1forx=-2蟺,x=0andx=2蟺g(x)=-1forx=-蟺andx=蟺

07

Part (f) Step 1. Calculation

f(x)=32forx=-11蟺6,-蟺6,蟺6,11蟺6

08

Part (g) Step 1. Calculation

The x intercept is(2k+1)蟺2wherek鈭�I.

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