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Chapter 3: Q. 11 (page 136)

True or False If the average rate of change of a linear function is 23, then if yincreases by 3,xwill increase by2.

Short Answer

Expert verified

The given statement is false.

Step by step solution

01

Given information

If the average rate of change of a linear function is23 , then if yincreases by3 , xwill increase by2 .

02

Solution

Linear functions have a constant average rate of change. That is, the average rate of change of a linear function y=mx+bis

鈭�y鈭�x=m.

Here, 鈭�x=2and 鈭�y=3,then m=鈭�y鈭�x=32.

03

Final answer

Hence, the given statement is false.

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Most popular questions from this chapter

If the slope m of the graph of a linear function is________, the function is increasing over its domain.

Approximate the local maximum values and local minimum values of f(x)=x3-5x+1 on (-4,4). Determine where the function is increasing and where it is decreasing.

A projectile is fired from a cliff 200ftabove the water at an inclination of 45掳to the horizontal, with a muzzle velocity of role="math" localid="1647357108345" 50ft/s. The height h of the projectile above the water is modeled by

hx=-32x2502+x+200

where x is the horizontal distance of the projectile from the face of the cliff.

Part (a): At what horizontal distance from the face of the cliff is the height of the projectile a maximum?

Part (b): Find the maximum height of the projectile.

Part (c): At what horizontal distance from the face of the cliff will the projectile strike the water?

Part (d): Using a graphing utility, graph the function h,0鈮�x鈮�200.

Part (e): Use a graphing utility to verify the solutions found in parts (b) and (c).

Part (f): When the height of the projectile is 100ftabove the water, how far is it from the cliff?

Graph the function fby starting with the graph of y=x2and using transformations (shifting, compressing, stretching, and/or reflection). Verify your results using a graphing utility.

Hint: If necessary, write fin the form f(x)=a(x-h)2+k.

f(x)=2x2-4x+1

Explain why the inequality x2-x+1<0has the empty set as solution set.
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