Consider the following function:f(x)={−7x2+5x−58x2+4x+9ifx<6ifx≥6𝑓(𝑥)={−7𝑥2+5𝑥−5if𝑥<68𝑥2+4𝑥+9if𝑥≥6Step 1 of 2 : At what x-value is the function discontinuous?
Question
Consider the following function:f(x)={−7x2+5x−58x2+4x+9ifx<6ifx≥6𝑓(𝑥)={−7𝑥2+5𝑥−5if𝑥<68𝑥2+4𝑥+9if𝑥≥6Step 1 of 2 : At what x-value is the function discontinuous?
Solution
The function is discontinuous at x = 6. This is because the function is defined by two different equations on either side of x = 6, and these two equations do not necessarily have the same value at x = 6. To be continuous at a point, a function must be defined at that point, approach the same value from either side of that point, and be able to pass through that point without a break. If these conditions are not met, the function is discontinuous at that point.
Similar Questions
List the value(s) of 𝑥 at which 𝑓 is discontinuous.Group of answer choices−5,−2,1,3,4,5-7,1,3,4,5−4,5−5,−2,1
Which function has a discontinuity at x=3?Responsesf(x)={3x+1 for x<3x2+1 for x≥3𝑓(𝑥)={3𝑥+1 𝑓𝑜𝑟 𝑥<3𝑥2+1 𝑓𝑜𝑟 𝑥≥3f(x)={3x+1 for x<3x2+1 for x≥3𝑓(𝑥)={3𝑥+1 𝑓𝑜𝑟 𝑥<3𝑥2+1 𝑓𝑜𝑟 𝑥≥3f(x)=|x−3|+2𝑓(𝑥)=|𝑥−3|+2f of x is equal to start absolute value x minus 3 end absolute value plus 2f(x)=x−3x2𝑓(𝑥)=𝑥−3𝑥2f of x is equal to the fraction with numerator x minus 3 and denominator x squaredf(x)=x+2x2−9
ist the value(s) of 𝑥 at which 𝑓 is discontinuous.
irst, sketch a graph of the following piecewise function.𝑓(𝑥)=⎧⎩⎨⎪⎪𝑥0𝑥𝑥<00≤𝑥<11≤𝑥Determine whether there are any points of discontinuity and write the x-values
Let be some fixed parameter. The following function is discontinuous at .Question 5Select one:TrueFalse
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.