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SAT Math : SAT Mathematics

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Example Questions

Example Question #2831 : Sat Mathematics

f(x) = 4x + 17

Solve f(x) for the equation above for x = 3.

Possible Answers:

Correct answer:

Explanation:

The correct answer is 29. We plug in 3 into the equation above and solve for x. So we find that f(x) = 4(3) + 17. 12 + 17 = 29

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Example Question #86 : How To Find F(X)

Define a function as follows:

f(x) = |2x - 7| + 19 .

If f(c)= f(3) and $c \ne 3$ , evaluate .

Possible Answers:

c= 16

c= 23

c= -3

c= 4

c= -4

Correct answer:

c= 4

Explanation:

f(x) = |2x - 7| + 19 , so

$f(3) = |2 \cdot 3 - 7| + 19 = |6-7 | + 19 = |-1| + 19 = 1 + 19 = 20$

Therefore, solve the equation

f(c)=20 for :

|2c - 7| + 19 = 20

|2c - 7| + 19- 19 = 20 - 19

|2c - 7| =1

Either 2c-7 = -1 or 2c-7 = 1 ; solve each.

2c-7 = -1

2c-7 + 7 = -1+ 7

2c = 6

c= 3 , which we toss out:

2c-7 = 1

2c-7 +7= 1+7

2c = 8

c = 4 , which we accept.

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Example Question #1056 : Algebra

Function 4

Define to be the function graphed above.

Give the -intercept of the graph of the function , which is defined as

g(x) = 5 - f(x) .

Possible Answers:

(0, -1)

(0, -9)

(0,1)

(0,9)

$\left ( 0, -\frac{1}{2} \right )$

Correct answer:

(0,9)

Explanation:

The -intercept of a function is the point at which x = 0 , so we can find this by evaluating g(0) .

g(x) = 5 - f(x)

g(0) = 5 - f(0)

From the diagram, it can be seen that f(0) = -4 , so

g(0) = 5 - (-4) = 9

The -intercept of the graph of is (0,9) .

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Example Question #1056 : Algebra

Function 4

Define to be the function graphed above.

Give the -intercept of the graph of the function , which is defined as

g(x) = f(4x) .

Possible Answers:

(0, 1)

(0, 8)

The correct answer is not given among the other four responses.

(0,0)

(0, 16)

Correct answer:

The correct answer is not given among the other four responses.

Explanation:

The -intercept of a function is the point at which x = 0 , so we can find this by evaluating g(0) .

g(x) = f(4x)

$g(0) = f(4 \cdot 0) = f (0)$

From the diagram, it can be seen that f(0) = -4 , so g(0) = -4 , and the -intercept of the graph of the function is the point (0, -4) . This is not among the given responses.

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Example Question #87 : How To Find F(X)

Function 4

Define to be the function graphed above.

Which of the following is an -intercept of the graph of the function , if is defined as

g(x)= f(x)+3 ?

Possible Answers:

$\left ( 2 \frac{1}{2}, 0\right )$

The graph of has no -intercept.

(-1,0)

$\left ( -6 \frac{1}{2}, 0\right )$

$\left ( - \frac{1}{2}, 0\right )$

Correct answer:

$\left ( - \frac{1}{2}, 0\right )$

Explanation:

An -intercept of the graph of has as its -coordinate a value such that

g(x) = 0 ,

or, equivalently,

f(x)+3 = 0

f(x) = -3

From the diagram below, it can be seen that if f(x) = -3 , then $x =-\frac{1}{2}$ or x = 2 .

Function 4a

Therefore, the graph of has two -intercepts, $\left ( - \frac{1}{2}, 0\right )$ and (2, 0) .

The correct choice is therefore $\left ( - \frac{1}{2}, 0\right )$ .

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Example Question #86 : How To Find F(X)

Function 4

Define to be the function graphed above.

Give the -intercept of the graph of the function , which is defined as

g(x) = f(x+ 3)

Possible Answers:

(0, -2)

$\left ( 0, -2 \frac{1}{2}\right )$

The graph of has no -intercept.

(0, -6)

(0,2)

Correct answer:

$\left ( 0, -2 \frac{1}{2}\right )$

Explanation:

The -intercept of a function is the point at which x = 0 , so we can find this by evaluating g(0) .

g(x) = f(x+ 3)

g(0) = f(0+ 3) = f(3)

As can be seen in the diagram below, $f(3) = -2\frac{1}{2}$ .

Function 4a

The -intercept is $\left ( 0, -2 \frac{1}{2}\right )$ .

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Example Question #131 : Algebraic Functions

Two functions

Define and to be the functions graphed above. Evaluate

$\left (g^{-1} \circ f \right ) (5)$ .

Possible Answers:

$\left (g^{-1} \circ f \right ) (5) = -5$

The expression is not defined.

$\left (g^{-1} \circ f \right ) (5) = -3$

$\left (g^{-1} \circ f \right ) (5) = -4$

$\left (g^{-1} \circ f \right ) (5) = 1$

Correct answer:

The expression is not defined.

Explanation:

It can be seen below that a horizontal line can be drawn through two points of the graph of .

Hlt

fails the Horizontal Line Test, which means that has no inverse. $g^{-1}$ does not exist, so the expression $\left (g^{-1} \circ f \right ) (5)$ is undefined.

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Example Question #1061 : Algebra

Function 4

Define as the function graphed above. Define function g (x) = 3x - 5 .

Evaluate $\left (g \circ f \right ) (3)$ .

Possible Answers:

3 is not in the domain of $g \circ f$ .

$\left (g \circ f \right ) (3) = 4$

$\left (g \circ f \right ) (3) = -2 \frac{1}{2}$

$\left (g \circ f \right ) (3) = -12 \frac{1}{2}$

$\left (g \circ f \right ) (3) = -2$

Correct answer:

$\left (g \circ f \right ) (3) = -12 \frac{1}{2}$

Explanation:

$\left (g \circ f \right ) (3) = g \left [ f (3)\right ]$ .

As can be seen in the diagram below, $f(3) = -2\frac{1}{2} = -\frac{5}{2}$ . Function 4a

Therefore,

$\left (g \circ f \right ) (3) = g \left ( - \frac{5}{2}\right )$

g (x) = 3x - 5 , so

$g \left ( - \frac{5}{2}\right ) = 3\left ( - \frac{5}{2}\right ) -5$

$= - \frac{15}{2} -5$

$= - 7 \frac{1}{2}-5$

$= -12\frac{1}{2}$

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Example Question #132 : Algebraic Functions

Two functions

Define and to be the functions graphed above.

Evaluate $(f \circ g ) (4)$

Possible Answers:

$\left (f \circ g \right ) (4) = -3$

$\left (f \circ g \right ) (4) = -6$

$\left (f \circ g \right ) (4) = -2$

4 is not in the domain of $f \circ g$ .

$\left (f \circ g \right ) (4) = -3 \frac{1}{6}$

Correct answer:

$\left (f \circ g \right ) (4) = -2$

Explanation:

$\left (f \circ g \right ) (4) = f \left [ g (4)\right ]$ .

From the diagram below, it can be seen that g(4) = -4

Two functions g 1

Therefore, $\left (f \circ g \right ) (4) = f (-4)$ .

From the diagram below, it can be seen that

f(-4) = -2 .

Two functions f

Therefore, the correct response is that $\left (f \circ g \right ) (4) = -2$ .

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Example Question #133 : Algebraic Functions

Two functions

Define and to be the functions graphed above. Evaluate

$\left (f^{-1} \circ g \right ) (4)$

Possible Answers:

$\left (f ^{-1} \circ g \right ) (4) = -1$

$\left (f ^{-1} \circ g \right ) (4) = -20$

$\left (f ^{-1} \circ g \right ) (4) = -8$

$\left (f ^{-1} \circ g \right ) (4) = 2$

$\left (f^{-1} \circ g \right ) (4)$ is undefined.

Correct answer:

$\left (f ^{-1} \circ g \right ) (4) = -8$

Explanation:

$\left (f ^{-1}\circ g \right ) (4) = f^{-1} \left [ g (4)\right ]$ .

From the diagram below, it can be seen that g(4) = -4

Two functions g 1

Therefore, $\left (f ^{-1} \circ g \right ) (4) = f^{-1} (-4)$ .

From the diagram below, it can be seen that

f(-8) = -4 .

Two functions f

so, by definition,

$f ^{-1} (-4)= -8$ .

Therefore, the correct response is that

$\left (f ^{-1} \circ g \right ) (4) = -8$ .

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SAT Math : SAT Mathematics

Study concepts, example questions & explanations for SAT Math

All SAT Math Resources

Example Questions

Example Question #2831 : Sat Mathematics

Example Question #86 : How To Find F(X)

Example Question #1056 : Algebra

Example Question #1056 : Algebra

Example Question #87 : How To Find F(X)

Example Question #86 : How To Find F(X)

Example Question #131 : Algebraic Functions

Example Question #1061 : Algebra

Example Question #132 : Algebraic Functions

Example Question #133 : Algebraic Functions

All SAT Math Resources

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