GMAT Math : x and y intercept

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Example Question #101 : Coordinate Geometry

What are the and intercepts of the function $y= \ln(x+3)$ ?

Possible Answers:

y-intercept at (-2, 0)

x-intercept at (0,3)

None of the other answers

y-intercept at (0,0)

x-intercept at (0,0)

y-intercept at (0,2)

x-intercept at (-3,2)

Correct answer:

None of the other answers

Explanation:

The correct answer is

y-intercept at $(0,\ln(3))$

x-intercept at (-2,0)

To find the y-intercept, we plug in for and solve for

So we have $y = \ln(3+0) = \ln(3)$ . This is as simplified as we can get.

To find the x-intercept, we plug in for and solve for

So we have $0 = \ln(x+3)$

$e^0 = e^{\ln(x+3)}$ (Exponentiate both sides)

1 = x+3 ( e^0 is 1, and cancel the and ln on the right side)

x= -2

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Example Question #102 : Coordinate Geometry

Fill in the circle with a number so that the graph of the resulting equation has -intercept (0,5) :

$4 x+ \bigcirc y = 18$

Possible Answers:

$\frac{5}{18}$

$\frac{18 }{5}$

$\frac{5}{4}$

$\frac{4}{5}$

Correct answer:

$\frac{18 }{5}$

Explanation:

Let be the number in the circle. The equation can be written as

4 x+N y = 18

Substitute 0 for and 5 for ; the equation becomes

$4 \cdot 0+N \cdot 5 = 18$

0+5N = 18

5N = 18

$N = \frac{18 }{5}$

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Example Question #11 : Calculating X Or Y Intercept

Fill in the circle with a number so that the graph of the resulting equation has -intercept (6,0) :

$4x+5y = \bigcirc$

Possible Answers:

The graph cannot have (6,0) as its -intercept regardless of the value written in the circle.

$\frac{3}{2}$

$\frac{6}{5}$

Correct answer:

Explanation:

Let be the number in the circle. The equation can be written as

4x+5y = N

Substitute 0 for and 6 for ; the resulting equation is

$4 \cdot 6+5 \cdot 0 = N$

N = 24 + 0 = 24

24 is the correct choice.

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Example Question #12 : Calculating X Or Y Intercept

Fill in the circle with a number so that the graph of the resulting equation has -intercept (-3,0) :

$\bigcirc x+ 5 y = 18$

Possible Answers:

The graph cannot have (-3,0) as its -intercept regardless of the value written in the circle.

$-\frac{6}{5}$

$-\frac{5}{6}$

Correct answer:

Explanation:

Let be the number in the circle. The equation can be written as

N x+ 5 y = 18

Substitute 0 for and for ; the resulting equation is

$N (-3)+ 5 \cdot 0= 18$

-3N + 0= 18

-3N = 18

N = -6

is the correct choice.

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Example Question #13 : Calculating X Or Y Intercept

Fill in the circle with a number so that the graph of the resulting equation has -intercept (5,0) :

$4 x+ \bigcirc y = 18$

Possible Answers:

$-\frac{5}{4}$

The graph cannot have (5,0) as its -intercept regardless of the value written in the circle.

$-\frac{9}{10}$

$-\frac{18}{5}$

Correct answer:

The graph cannot have (5,0) as its -intercept regardless of the value written in the circle.

Explanation:

Let be the number in the circle. The equation can be written as

4 x+N y = 18

Substitute 0 for ; the resulting equation is

$4 x+N \cdot 0 = 18$

4x= 18

$x = \frac{9}{2}$

The -intercept is $\left ( \frac{9}{2}, 0 \right )$ regardless of what number is written in the circle.

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Example Question #14 : Calculating X Or Y Intercept

Fill in the circle with a number so that the graph of the resulting equation has -intercept (0, 7) :

$4x+5y = \bigcirc$

Possible Answers:

$\frac{7}{4}$

$\frac{7}{5}$

Correct answer:

Explanation:

Let be the number in the circle. The equation can be written as

4x+5y = N

Substitute 7 for and 0 for ; the resulting equation is

$4 \cdot 0+5 \cdot 7= N$

N = 0+35

N = 35

35 is the correct choice.

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Example Question #15 : Calculating X Or Y Intercept

Fill in the circle so that the graph of the resulting equation has no -intercepts:

$y = 4x^{2}+ 6 x + \bigcirc$

Possible Answers:

The graph will have at least one -intercept regardless of the value written in the circle.

Correct answer:

Explanation:

Let be the number in the circle. Then the equation can be rewritten as

$y = 4x^{2}+ 6 x + C$

Substitute 0 for and the equation becomes

$4x^{2}+ 6 x + C = 0$

Equivalently, we are seeking a value of for which this equation has no real solutions. This happens in a quadratic equation $Ax^{2}+ Bx+ C = 0$ if and only if

$B^{2}-4AC < 0$

Replacing with 4 and with 6, this becomes

$6^{2}-4 \cdot 4 \cdot C < 0$

36-16C < 0

16C > 36

$C > \frac{36}{16} = \frac{9}{4}$

Therefore, must be greater than $\frac{9}{4}$ . The only choice fitting this requirement is 4, so this is correct.

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Example Question #16 : Calculating X Or Y Intercept

Fill in the circle so that the graph of the resulting equation has exactly one -intercept:

$y = 4x^{2}+ \bigcirc x + 8$

Possible Answers:

None of the other choices is correct.

Correct answer:

None of the other choices is correct.

Explanation:

Let be the number in the circle. Then the equation can be rewritten as

$y = 4x^{2}+ Bx + 8$

Substitute 0 for and the equation becomes

$4x^{2}+ Bx + 8 = 0$

Equivalently, we are seeking a value of for which this equation has exactly one solution. This happens in a quadratic equation $Ax^{2}+ Bx+ C = 0$ if and only if

$B^{2}-4AC = 0$

Replacing with 4 and with 8, this becomes

$B^{2}-4 \cdot 4 \cdot 8 = 0$

$B^{2}-128= 0$

$B^{2}=128$

$B= \pm \sqrt{128} = \pm \sqrt{64} \cdot \sqrt{2} = \pm 8 \sqrt{2}$

Therefore, either $B=- 8 \sqrt{2}$ or $B= 8 \sqrt{2}$ .

Neither is a choice.

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Example Question #17 : Calculating X Or Y Intercept

Find the $y\textup{-intercept}$ for the following equation:

3x-2y=6

Possible Answers:

(-3,0)

(0,-3)

(0,3)

(3,0)

Correct answer:

(0,-3)

Explanation:

To find the $y\textup{-intercept}$ , you must put the equation into slope intercept form:

y=mx+b where (0,b) is the intercept.

Thus,

3x-2y=6

-2y=-3x+6

$y=\frac{3}2{x-3}$

Therefore, your $y\textup{-intercept}$ is (0,-3)

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Example Question #11 : X And Y Intercept

Find where g(x) crosses the y-axis.

g(x)=5x^3-6x^2-5x+945

Possible Answers:

945

Correct answer:

945

Explanation:

Find where g(x) crosses the y-axis.

g(x)=5x^3-6x^2-5x+945

A function will cross the y-axis wherever x is equal to 0. This may be easier to see on a graph, but it can be thought of intuitively as well. If x is 0, then we are neither left nor right of the y-axis. This means we must be on the y-axis.

So, find g(0)

g(0)=5(0)^3-6(0)^2-5(0)+945=945

So our answer is 945.

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GMAT Math : x and y intercept

Study concepts, example questions & explanations for GMAT Math

All GMAT Math Resources

Example Questions

Example Question #101 : Coordinate Geometry

Example Question #102 : Coordinate Geometry

Example Question #11 : Calculating X Or Y Intercept

Example Question #12 : Calculating X Or Y Intercept

Example Question #13 : Calculating X Or Y Intercept

Example Question #14 : Calculating X Or Y Intercept

Example Question #15 : Calculating X Or Y Intercept

Example Question #16 : Calculating X Or Y Intercept

Example Question #17 : Calculating X Or Y Intercept

Example Question #11 : X And Y Intercept

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