Answer: Choice D) x intercept of f(x) is larger then the x intercept of g(x)
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Explanation:
A) False. The x intercept of f is 1 while the x intercept of g is -1. The x intercept happens when y = 0. Visually, this is where the graph crosses the x axis.
B) False. The y intercept of f(x) is -1, compared to the y intercept of g(x) is +1. The y intercept happens when x = 0, which is when the graph crosses the y axis.
C) False. The y intercept of f(x) is actually smaller than the y intercept for g(x)
D) True. The x intercept of f(x) is larger than the x intercept of g(x). Compare 1 and -1, which are the x intercepts for f and g in that order.
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Solution:</h3>
A linear function is a straight line formed on a coordinate plane.
<u>To classify an equation as a linear function:</u>
- It must not have any exponent in the equation.
- If there is a fraction, the denominator of that fraction must not multiply by x.
If any of these two occurs in an equation, the line can form a curve in a line, which is a non-linear function. A non-linear function is a curved line formed on a coordinate plane.
<u>Option A - y = x³ + 1:</u>
- This equation has an exponent in the variable x. Hence, this is a non-linear function.
<u>Option B - 5x/6 = y - 4:</u>
- This equation has no exponents in the equation. Hence, this is a linear function and also our answer.
<u>Option C - y = 8x²</u>
- This equation has an exponent in the term 8x². Hence, this is a non-linear function.
<u>Option D - y = 1/5x</u>
- The denominator of the fraction on the RHS side is multiplied by x. Hence, this is not a linear function.
Hence, Option B is correct.
<u>Learn more about </u><u>linear functions</u><u>:</u> brainly.com/question/15253497
Answer:
(4, -25)
Step-by-step explanation:
One way to answer this is to put the equation into vertex form.
f(x)= x^2 -8x -9 . . . . . given
Add and subtract the square of half the x-coefficient:
f(x) = x^2 -8x +(-8/2)^2 -9 -(-8/2)^2
f(x) = x^2 -8x +16 -25
f(x) = (x -4)^2 -25
Comparing this to the vertex form of a quadratic:
f(x) = a(x -h)^2 +k
we find that (h, k) = (4, -25). This is the vertex.
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<em>Alternate solution</em>
The line of symmetry for ...
f(x) = ax^2 +bx +c
is given by x = -b/(2a). For your given quadratic that line is ...
x = -(-8)/(2(1)) = 4
Evaluating f(4) gives the y-coordinate:
f(4) = 4^2 -8·4 -9 = -25
The vertex is (x, y) = (4, -25).
Answer:
1,00000,00,00
Step-by-step explanation:
Answer:
26.4 km/hr
Step-by-step explanation:
Sofia and Diego drive to work.
For Sofia
We convert miles to km
Sofia drives 72 miles in 1.5 hours.
1 mile = 1.6 km
72 miles = x
x = 72 × 1.6 km
x = 115.2 km
We find the speed in km/hr
Speed = Distance /Time
= 115.2km/1.5 hours
= 76.8 km/hr
For Diego
Diego drives 126 km in 2 hour 30 min.
Speed = Distance/Time
Time = 2 hour 30 min = 2.5 hours
Speed = 126km/2.5 hours
= 50.4 km/hr
The difference between their average speeds in km/h is calculated as:
76.8 km/hr - 50.4 km/hr
= 26.4 km/hr
